Datasets:
Tasks:
Visual Question Answering
Modalities:
Image
Formats:
imagefolder
Languages:
English
Size:
1K - 10K
License:
| {"qid": 6300, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, 0], [2, -9], [2, 6]], "answer": {"point": [-1.75, -1.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 0), B=(2, -9), C=(2, 6). Find the circumradius.", "im_path": "/images_full/task_06300_circumcircle.png", "im_dots_path": "/images/task_06300_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.75, -1.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6301, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 3], [2, 4], [-6, 6]], "answer": {"point": [-1.25, 8.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 3), B=(2, 4), C=(-6, 6). Find the circumradius.", "im_path": "/images_full/task_06301_circumcircle.png", "im_dots_path": "/images/task_06301_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.25, 8.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6302, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[8, 3], [7, -10], [4, -9]], "answer": {"point": [7.5, -3.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, 3), B=(7, -10), C=(4, -9). Find the circumradius.", "im_path": "/images_full/task_06302_circumcircle.png", "im_dots_path": "/images/task_06302_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [7.5, -3.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6303, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, -3], [2, -5], [-1, 5]], "answer": {"point": [-0.6538461538461539, -0.34615384615384615]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -3), B=(2, -5), C=(-1, 5). Find the circumradius.", "im_path": "/images_full/task_06303_circumcircle.png", "im_dots_path": "/images/task_06303_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.6538461538461539, -0.34615384615384615]}, "choices": null, "image_choices": null} | |
| {"qid": 6304, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 7], [-10, -1], [-7, 4]], "answer": {"point": [3.3181818181818183, -5.590909090909091]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 7), B=(-10, -1), C=(-7, 4). Find the circumradius.", "im_path": "/images_full/task_06304_circumcircle.png", "im_dots_path": "/images/task_06304_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.3181818181818183, -5.590909090909091]}, "choices": null, "image_choices": null} | |
| {"qid": 6305, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, -9], [-4, -5], [5, 2]], "answer": {"point": [-77.66666666666667, 99.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, -9), B=(-4, -5), C=(5, 2). Find the circumradius.", "im_path": "/images_full/task_06305_circumcircle.png", "im_dots_path": "/images/task_06305_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-77.66666666666667, 99.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6306, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, 8], [9, 9], [-2, 5]], "answer": {"point": [0.5943396226415094, 14.99056603773585]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 8), B=(9, 9), C=(-2, 5). Find the circumradius.", "im_path": "/images_full/task_06306_circumcircle.png", "im_dots_path": "/images/task_06306_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.5943396226415094, 14.99056603773585]}, "choices": null, "image_choices": null} | |
| {"qid": 6307, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, 1], [-6, -4], [-10, -9]], "answer": {"point": [13.166666666666666, -23.433333333333334]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 1), B=(-6, -4), C=(-10, -9). Find the circumradius.", "im_path": "/images_full/task_06307_circumcircle.png", "im_dots_path": "/images/task_06307_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [13.166666666666666, -23.433333333333334]}, "choices": null, "image_choices": null} | |
| {"qid": 6308, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, 5], [7, 3], [7, 0]], "answer": {"point": [3.8333333333333335, 1.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 5), B=(7, 3), C=(7, 0). Find the circumradius.", "im_path": "/images_full/task_06308_circumcircle.png", "im_dots_path": "/images/task_06308_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.8333333333333335, 1.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6309, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, -8], [3, 8], [1, -3]], "answer": {"point": [-9.0, 4.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, -8), B=(3, 8), C=(1, -3). Find the circumradius.", "im_path": "/images_full/task_06309_circumcircle.png", "im_dots_path": "/images/task_06309_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-9.0, 4.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6310, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, 4], [7, -2], [2, -6]], "answer": {"point": [-4.833333333333333, 7.666666666666667]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, 4), B=(7, -2), C=(2, -6). Find the circumradius.", "im_path": "/images_full/task_06310_circumcircle.png", "im_dots_path": "/images/task_06310_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.833333333333333, 7.666666666666667]}, "choices": null, "image_choices": null} | |
| {"qid": 6311, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 7], [1, -4], [-2, -4]], "answer": {"point": [-0.5, 4.681818181818182]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 7), B=(1, -4), C=(-2, -4). Find the circumradius.", "im_path": "/images_full/task_06311_circumcircle.png", "im_dots_path": "/images/task_06311_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.5, 4.681818181818182]}, "choices": null, "image_choices": null} | |
| {"qid": 6312, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 5], [5, 10], [-9, 9]], "answer": {"point": [-1.7535211267605635, 6.049295774647887]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 5), B=(5, 10), C=(-9, 9). Find the circumradius.", "im_path": "/images_full/task_06312_circumcircle.png", "im_dots_path": "/images/task_06312_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.7535211267605635, 6.049295774647887]}, "choices": null, "image_choices": null} | |
| {"qid": 6313, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, -3], [-8, 8], [5, 3]], "answer": {"point": [-3.6153846153846154, -0.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, -3), B=(-8, 8), C=(5, 3). Find the circumradius.", "im_path": "/images_full/task_06313_circumcircle.png", "im_dots_path": "/images/task_06313_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-3.6153846153846154, -0.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6314, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, -6], [-7, 3], [-2, -5]], "answer": {"point": [-4.913793103448276, -1.2586206896551724]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, -6), B=(-7, 3), C=(-2, -5). Find the circumradius.", "im_path": "/images_full/task_06314_circumcircle.png", "im_dots_path": "/images/task_06314_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.913793103448276, -1.2586206896551724]}, "choices": null, "image_choices": null} | |
| {"qid": 6315, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, -7], [1, -7], [8, -6]], "answer": {"point": [-3.5, 49.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, -7), B=(1, -7), C=(8, -6). Find the circumradius.", "im_path": "/images_full/task_06315_circumcircle.png", "im_dots_path": "/images/task_06315_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-3.5, 49.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6316, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, 10], [-7, 10], [6, -5]], "answer": {"point": [-1.5, 1.6333333333333333]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 10), B=(-7, 10), C=(6, -5). Find the circumradius.", "im_path": "/images_full/task_06316_circumcircle.png", "im_dots_path": "/images/task_06316_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.5, 1.6333333333333333]}, "choices": null, "image_choices": null} | |
| {"qid": 6317, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 4], [1, 4], [6, -9]], "answer": {"point": [3.5, -2.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 4), B=(1, 4), C=(6, -9). Find the circumradius.", "im_path": "/images_full/task_06317_circumcircle.png", "im_dots_path": "/images/task_06317_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.5, -2.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6318, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, 6], [-2, 3], [-4, -10]], "answer": {"point": [44.357142857142854, -10.785714285714286]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, 6), B=(-2, 3), C=(-4, -10). Find the circumradius.", "im_path": "/images_full/task_06318_circumcircle.png", "im_dots_path": "/images/task_06318_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [44.357142857142854, -10.785714285714286]}, "choices": null, "image_choices": null} | |
| {"qid": 6319, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 3], [5, 0], [-8, 4]], "answer": {"point": [-0.9883720930232558, 3.6627906976744184]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 3), B=(5, 0), C=(-8, 4). Find the circumradius.", "im_path": "/images_full/task_06319_circumcircle.png", "im_dots_path": "/images/task_06319_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.9883720930232558, 3.6627906976744184]}, "choices": null, "image_choices": null} | |
| {"qid": 6320, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, 4], [-6, -8], [7, -2]], "answer": {"point": [-0.2619047619047619, -3.3492063492063493]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, 4), B=(-6, -8), C=(7, -2). Find the circumradius.", "im_path": "/images_full/task_06320_circumcircle.png", "im_dots_path": "/images/task_06320_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.2619047619047619, -3.3492063492063493]}, "choices": null, "image_choices": null} | |
| {"qid": 6321, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 3], [-1, 4], [-3, 10]], "answer": {"point": [4.568965517241379, 9.189655172413794]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 3), B=(-1, 4), C=(-3, 10). Find the circumradius.", "im_path": "/images_full/task_06321_circumcircle.png", "im_dots_path": "/images/task_06321_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [4.568965517241379, 9.189655172413794]}, "choices": null, "image_choices": null} | |
| {"qid": 6322, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 8], [1, 6], [-4, -7]], "answer": {"point": [-5.214285714285714, 0.9285714285714286]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 8), B=(1, 6), C=(-4, -7). Find the circumradius.", "im_path": "/images_full/task_06322_circumcircle.png", "im_dots_path": "/images/task_06322_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-5.214285714285714, 0.9285714285714286]}, "choices": null, "image_choices": null} | |
| {"qid": 6323, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, 5], [-2, 8], [-5, -2]], "answer": {"point": [-0.3987341772151899, 2.069620253164557]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, 5), B=(-2, 8), C=(-5, -2). Find the circumradius.", "im_path": "/images_full/task_06323_circumcircle.png", "im_dots_path": "/images/task_06323_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.3987341772151899, 2.069620253164557]}, "choices": null, "image_choices": null} | |
| {"qid": 6324, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 2], [-1, 6], [-4, -9]], "answer": {"point": [-1.2096774193548387, -1.7580645161290323]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 2), B=(-1, 6), C=(-4, -9). Find the circumradius.", "im_path": "/images_full/task_06324_circumcircle.png", "im_dots_path": "/images/task_06324_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.2096774193548387, -1.7580645161290323]}, "choices": null, "image_choices": null} | |
| {"qid": 6325, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, 0], [1, 1], [-9, 0]], "answer": {"point": [-4.0, 0.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, 0), B=(1, 1), C=(-9, 0). Find the circumradius.", "im_path": "/images_full/task_06325_circumcircle.png", "im_dots_path": "/images/task_06325_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.0, 0.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6326, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, -8], [10, 9], [-7, 2]], "answer": {"point": [2.973684210526316, 1.9210526315789473]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, -8), B=(10, 9), C=(-7, 2). Find the circumradius.", "im_path": "/images_full/task_06326_circumcircle.png", "im_dots_path": "/images/task_06326_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [2.973684210526316, 1.9210526315789473]}, "choices": null, "image_choices": null} | |
| {"qid": 6327, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 0], [-9, -4], [-6, -4]], "answer": {"point": [-7.5, 20.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 0), B=(-9, -4), C=(-6, -4). Find the circumradius.", "im_path": "/images_full/task_06327_circumcircle.png", "im_dots_path": "/images/task_06327_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-7.5, 20.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6328, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 3], [-1, 8], [0, -3]], "answer": {"point": [-2.2439024390243905, 2.341463414634146]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 3), B=(-1, 8), C=(0, -3). Find the circumradius.", "im_path": "/images_full/task_06328_circumcircle.png", "im_dots_path": "/images/task_06328_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.2439024390243905, 2.341463414634146]}, "choices": null, "image_choices": null} | |
| {"qid": 6329, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, 10], [-1, 6], [-6, 7]], "answer": {"point": [-3.323529411764706, 7.382352941176471]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, 10), B=(-1, 6), C=(-6, 7). Find the circumradius.", "im_path": "/images_full/task_06329_circumcircle.png", "im_dots_path": "/images/task_06329_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-3.323529411764706, 7.382352941176471]}, "choices": null, "image_choices": null} | |
| {"qid": 6330, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, -7], [-10, 10], [7, 9]], "answer": {"point": [-1.870503597122302, 3.2014388489208634]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, -7), B=(-10, 10), C=(7, 9). Find the circumradius.", "im_path": "/images_full/task_06330_circumcircle.png", "im_dots_path": "/images/task_06330_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.870503597122302, 3.2014388489208634]}, "choices": null, "image_choices": null} | |
| {"qid": 6331, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, -7], [0, 6], [-5, 2]], "answer": {"point": [3.5, -3.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, -7), B=(0, 6), C=(-5, 2). Find the circumradius.", "im_path": "/images_full/task_06331_circumcircle.png", "im_dots_path": "/images/task_06331_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.5, -3.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6332, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 3], [2, 8], [-6, 7]], "answer": {"point": [-1.803030303030303, 5.924242424242424]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 3), B=(2, 8), C=(-6, 7). Find the circumradius.", "im_path": "/images_full/task_06332_circumcircle.png", "im_dots_path": "/images/task_06332_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.803030303030303, 5.924242424242424]}, "choices": null, "image_choices": null} | |
| {"qid": 6333, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, -2], [-2, 3], [-8, 2]], "answer": {"point": [-4.181818181818182, -2.409090909090909]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, -2), B=(-2, 3), C=(-8, 2). Find the circumradius.", "im_path": "/images_full/task_06333_circumcircle.png", "im_dots_path": "/images/task_06333_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.181818181818182, -2.409090909090909]}, "choices": null, "image_choices": null} | |
| {"qid": 6334, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 0], [10, -5], [-8, -1]], "answer": {"point": [1.5555555555555556, -0.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 0), B=(10, -5), C=(-8, -1). Find the circumradius.", "im_path": "/images_full/task_06334_circumcircle.png", "im_dots_path": "/images/task_06334_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [1.5555555555555556, -0.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6335, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, 10], [-7, 1], [9, 7]], "answer": {"point": [0.7391304347826086, 4.695652173913044]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 10), B=(-7, 1), C=(9, 7). Find the circumradius.", "im_path": "/images_full/task_06335_circumcircle.png", "im_dots_path": "/images/task_06335_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.7391304347826086, 4.695652173913044]}, "choices": null, "image_choices": null} | |
| {"qid": 6336, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, -10], [7, 1], [1, 4]], "answer": {"point": [-0.13157894736842105, -5.7631578947368425]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, -10), B=(7, 1), C=(1, 4). Find the circumradius.", "im_path": "/images_full/task_06336_circumcircle.png", "im_dots_path": "/images/task_06336_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.13157894736842105, -5.7631578947368425]}, "choices": null, "image_choices": null} | |
| {"qid": 6337, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, -2], [0, -1], [1, -4]], "answer": {"point": [3.5, -1.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, -2), B=(0, -1), C=(1, -4). Find the circumradius.", "im_path": "/images_full/task_06337_circumcircle.png", "im_dots_path": "/images/task_06337_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.5, -1.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6338, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, -5], [4, 6], [-10, -7]], "answer": {"point": [-0.2543103448275862, -3.456896551724138]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, -5), B=(4, 6), C=(-10, -7). Find the circumradius.", "im_path": "/images_full/task_06338_circumcircle.png", "im_dots_path": "/images/task_06338_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.2543103448275862, -3.456896551724138]}, "choices": null, "image_choices": null} | |
| {"qid": 6339, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, -1], [-2, 8], [-5, -2]], "answer": {"point": [-4.175675675675675, 3.2027027027027026]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -1), B=(-2, 8), C=(-5, -2). Find the circumradius.", "im_path": "/images_full/task_06339_circumcircle.png", "im_dots_path": "/images/task_06339_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.175675675675675, 3.2027027027027026]}, "choices": null, "image_choices": null} | |
| {"qid": 6340, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, 6], [-2, -2], [-9, 7]], "answer": {"point": [-2.6363636363636362, 4.7272727272727275]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 6), B=(-2, -2), C=(-9, 7). Find the circumradius.", "im_path": "/images_full/task_06340_circumcircle.png", "im_dots_path": "/images/task_06340_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.6363636363636362, 4.7272727272727275]}, "choices": null, "image_choices": null} | |
| {"qid": 6341, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, -6], [8, -9], [-7, 5]], "answer": {"point": [-10.112903225806452, -13.370967741935484]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, -6), B=(8, -9), C=(-7, 5). Find the circumradius.", "im_path": "/images_full/task_06341_circumcircle.png", "im_dots_path": "/images/task_06341_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-10.112903225806452, -13.370967741935484]}, "choices": null, "image_choices": null} | |
| {"qid": 6342, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[6, 7], [-2, 7], [-10, -3]], "answer": {"point": [2.0, -4.4]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(6, 7), B=(-2, 7), C=(-10, -3). Find the circumradius.", "im_path": "/images_full/task_06342_circumcircle.png", "im_dots_path": "/images/task_06342_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [2.0, -4.4]}, "choices": null, "image_choices": null} | |
| {"qid": 6343, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, -7], [-6, 9], [-8, 1]], "answer": {"point": [2.0555555555555554, 2.736111111111111]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -7), B=(-6, 9), C=(-8, 1). Find the circumradius.", "im_path": "/images_full/task_06343_circumcircle.png", "im_dots_path": "/images/task_06343_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [2.0555555555555554, 2.736111111111111]}, "choices": null, "image_choices": null} | |
| {"qid": 6344, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, -10], [10, 5], [-7, -7]], "answer": {"point": [19.944444444444443, -27.12962962962963]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, -10), B=(10, 5), C=(-7, -7). Find the circumradius.", "im_path": "/images_full/task_06344_circumcircle.png", "im_dots_path": "/images/task_06344_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [19.944444444444443, -27.12962962962963]}, "choices": null, "image_choices": null} | |
| {"qid": 6345, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, -10], [-6, -5], [8, 3]], "answer": {"point": [6.161290322580645, -10.03225806451613]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -10), B=(-6, -5), C=(8, 3). Find the circumradius.", "im_path": "/images_full/task_06345_circumcircle.png", "im_dots_path": "/images/task_06345_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [6.161290322580645, -10.03225806451613]}, "choices": null, "image_choices": null} | |
| {"qid": 6346, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 6], [-4, 2], [10, -10]], "answer": {"point": [7.5, 1.25]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 6), B=(-4, 2), C=(10, -10). Find the circumradius.", "im_path": "/images_full/task_06346_circumcircle.png", "im_dots_path": "/images/task_06346_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [7.5, 1.25]}, "choices": null, "image_choices": null} | |
| {"qid": 6347, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, -2], [3, -8], [-6, -8]], "answer": {"point": [-1.5, -4.166666666666667]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -2), B=(3, -8), C=(-6, -8). Find the circumradius.", "im_path": "/images_full/task_06347_circumcircle.png", "im_dots_path": "/images/task_06347_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.5, -4.166666666666667]}, "choices": null, "image_choices": null} | |
| {"qid": 6348, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, 6], [10, -9], [8, 8]], "answer": {"point": [11.318181818181818, -0.22727272727272727]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, 6), B=(10, -9), C=(8, 8). Find the circumradius.", "im_path": "/images_full/task_06348_circumcircle.png", "im_dots_path": "/images/task_06348_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [11.318181818181818, -0.22727272727272727]}, "choices": null, "image_choices": null} | |
| {"qid": 6349, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, -9], [9, -5], [-9, 7]], "answer": {"point": [-1.0217391304347827, -0.532608695652174]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, -9), B=(9, -5), C=(-9, 7). Find the circumradius.", "im_path": "/images_full/task_06349_circumcircle.png", "im_dots_path": "/images/task_06349_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.0217391304347827, -0.532608695652174]}, "choices": null, "image_choices": null} | |
| {"qid": 6350, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, 0], [-6, 4], [3, -3]], "answer": {"point": [2.6363636363636362, 5.818181818181818]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, 0), B=(-6, 4), C=(3, -3). Find the circumradius.", "im_path": "/images_full/task_06350_circumcircle.png", "im_dots_path": "/images/task_06350_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [2.6363636363636362, 5.818181818181818]}, "choices": null, "image_choices": null} | |
| {"qid": 6351, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[3, 9], [7, 0], [0, 5]], "answer": {"point": [4.895348837209302, 4.453488372093023]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, 9), B=(7, 0), C=(0, 5). Find the circumradius.", "im_path": "/images_full/task_06351_circumcircle.png", "im_dots_path": "/images/task_06351_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [4.895348837209302, 4.453488372093023]}, "choices": null, "image_choices": null} | |
| {"qid": 6352, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 8], [10, 5], [2, 10]], "answer": {"point": [-1.147887323943662, -3.936619718309859]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 8), B=(10, 5), C=(2, 10). Find the circumradius.", "im_path": "/images_full/task_06352_circumcircle.png", "im_dots_path": "/images/task_06352_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.147887323943662, -3.936619718309859]}, "choices": null, "image_choices": null} | |
| {"qid": 6353, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 0], [-8, -6], [-2, -8]], "answer": {"point": [-3.6666666666666665, -3.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 0), B=(-8, -6), C=(-2, -8). Find the circumradius.", "im_path": "/images_full/task_06353_circumcircle.png", "im_dots_path": "/images/task_06353_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-3.6666666666666665, -3.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6354, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, -9], [10, 5], [-6, 9]], "answer": {"point": [0.45652173913043476, 0.8260869565217391]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, -9), B=(10, 5), C=(-6, 9). Find the circumradius.", "im_path": "/images_full/task_06354_circumcircle.png", "im_dots_path": "/images/task_06354_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.45652173913043476, 0.8260869565217391]}, "choices": null, "image_choices": null} | |
| {"qid": 6355, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 10], [6, -6], [-8, 10]], "answer": {"point": [-4.0, -0.625]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 10), B=(6, -6), C=(-8, 10). Find the circumradius.", "im_path": "/images_full/task_06355_circumcircle.png", "im_dots_path": "/images/task_06355_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.0, -0.625]}, "choices": null, "image_choices": null} | |
| {"qid": 6356, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 6], [-7, -3], [-2, -8]], "answer": {"point": [1.54, 0.54]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 6), B=(-7, -3), C=(-2, -8). Find the circumradius.", "im_path": "/images_full/task_06356_circumcircle.png", "im_dots_path": "/images/task_06356_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [1.54, 0.54]}, "choices": null, "image_choices": null} | |
| {"qid": 6357, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-6, 8], [0, -2], [-3, -9]], "answer": {"point": [-10.63888888888889, -1.5833333333333333]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-6, 8), B=(0, -2), C=(-3, -9). Find the circumradius.", "im_path": "/images_full/task_06357_circumcircle.png", "im_dots_path": "/images/task_06357_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-10.63888888888889, -1.5833333333333333]}, "choices": null, "image_choices": null} | |
| {"qid": 6358, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[3, -1], [-1, -8], [0, 0]], "answer": {"point": [0.3, -4.1]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(3, -1), B=(-1, -8), C=(0, 0). Find the circumradius.", "im_path": "/images_full/task_06358_circumcircle.png", "im_dots_path": "/images/task_06358_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.3, -4.1]}, "choices": null, "image_choices": null} | |
| {"qid": 6359, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, -1], [1, -6], [-6, -6]], "answer": {"point": [-2.5, -2.7]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, -1), B=(1, -6), C=(-6, -6). Find the circumradius.", "im_path": "/images_full/task_06359_circumcircle.png", "im_dots_path": "/images/task_06359_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.5, -2.7]}, "choices": null, "image_choices": null} | |
| {"qid": 6360, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 5], [-3, 5], [-9, -2]], "answer": {"point": [-6.0, 1.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 5), B=(-3, 5), C=(-9, -2). Find the circumradius.", "im_path": "/images_full/task_06360_circumcircle.png", "im_dots_path": "/images/task_06360_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-6.0, 1.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6361, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[8, -10], [-7, 5], [-2, 10]], "answer": {"point": [3.0, -0.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, -10), B=(-7, 5), C=(-2, 10). Find the circumradius.", "im_path": "/images_full/task_06361_circumcircle.png", "im_dots_path": "/images/task_06361_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.0, -0.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6362, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, -9], [9, -4], [-6, 6]], "answer": {"point": [0.8448275862068966, 0.017241379310344827]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -9), B=(9, -4), C=(-6, 6). Find the circumradius.", "im_path": "/images_full/task_06362_circumcircle.png", "im_dots_path": "/images/task_06362_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.8448275862068966, 0.017241379310344827]}, "choices": null, "image_choices": null} | |
| {"qid": 6363, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, -1], [-4, 8], [-9, -7]], "answer": {"point": [-0.875, -1.375]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, -1), B=(-4, 8), C=(-9, -7). Find the circumradius.", "im_path": "/images_full/task_06363_circumcircle.png", "im_dots_path": "/images/task_06363_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.875, -1.375]}, "choices": null, "image_choices": null} | |
| {"qid": 6364, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, 5], [0, 5], [-7, 7]], "answer": {"point": [-3.5, 6.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 5), B=(0, 5), C=(-7, 7). Find the circumradius.", "im_path": "/images_full/task_06364_circumcircle.png", "im_dots_path": "/images/task_06364_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-3.5, 6.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6365, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, -10], [-1, -8], [-8, 8]], "answer": {"point": [11.029411764705882, 6.794117647058823]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -10), B=(-1, -8), C=(-8, 8). Find the circumradius.", "im_path": "/images_full/task_06365_circumcircle.png", "im_dots_path": "/images/task_06365_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [11.029411764705882, 6.794117647058823]}, "choices": null, "image_choices": null} | |
| {"qid": 6366, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, -10], [-3, -7], [9, 2]], "answer": {"point": [5.5, -5.833333333333333]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, -10), B=(-3, -7), C=(9, 2). Find the circumradius.", "im_path": "/images_full/task_06366_circumcircle.png", "im_dots_path": "/images/task_06366_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [5.5, -5.833333333333333]}, "choices": null, "image_choices": null} | |
| {"qid": 6367, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, 5], [7, -5], [5, 0]], "answer": {"point": [12.25, -0.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 5), B=(7, -5), C=(5, 0). Find the circumradius.", "im_path": "/images_full/task_06367_circumcircle.png", "im_dots_path": "/images/task_06367_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [12.25, -0.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6368, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, -1], [5, -3], [-7, 10]], "answer": {"point": [3.601123595505618, 7.747191011235955]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, -1), B=(5, -3), C=(-7, 10). Find the circumradius.", "im_path": "/images_full/task_06368_circumcircle.png", "im_dots_path": "/images/task_06368_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [3.601123595505618, 7.747191011235955]}, "choices": null, "image_choices": null} | |
| {"qid": 6369, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 0], [10, 9], [-2, -2]], "answer": {"point": [-2.262376237623762, 10.331683168316832]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 0), B=(10, 9), C=(-2, -2). Find the circumradius.", "im_path": "/images_full/task_06369_circumcircle.png", "im_dots_path": "/images/task_06369_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.262376237623762, 10.331683168316832]}, "choices": null, "image_choices": null} | |
| {"qid": 6370, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-5, 8], [-10, 3], [6, 5]], "answer": {"point": [-1.4285714285714286, -0.5714285714285714]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-5, 8), B=(-10, 3), C=(6, 5). Find the circumradius.", "im_path": "/images_full/task_06370_circumcircle.png", "im_dots_path": "/images/task_06370_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.4285714285714286, -0.5714285714285714]}, "choices": null, "image_choices": null} | |
| {"qid": 6371, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, -8], [-10, -10], [4, -6]], "answer": {"point": [-2.3125, -10.40625]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, -8), B=(-10, -10), C=(4, -6). Find the circumradius.", "im_path": "/images_full/task_06371_circumcircle.png", "im_dots_path": "/images/task_06371_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.3125, -10.40625]}, "choices": null, "image_choices": null} | |
| {"qid": 6372, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 7], [0, 7], [10, -4]], "answer": {"point": [-4.0, -6.681818181818182]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 7), B=(0, 7), C=(10, -4). Find the circumradius.", "im_path": "/images_full/task_06372_circumcircle.png", "im_dots_path": "/images/task_06372_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-4.0, -6.681818181818182]}, "choices": null, "image_choices": null} | |
| {"qid": 6373, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, 5], [2, -4], [9, 3]], "answer": {"point": [-7.5, 12.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, 5), B=(2, -4), C=(9, 3). Find the circumradius.", "im_path": "/images_full/task_06373_circumcircle.png", "im_dots_path": "/images/task_06373_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-7.5, 12.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6374, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 3], [-6, -4], [-9, -6]], "answer": {"point": [29.5, -60.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 3), B=(-6, -4), C=(-9, -6). Find the circumradius.", "im_path": "/images_full/task_06374_circumcircle.png", "im_dots_path": "/images/task_06374_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [29.5, -60.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6375, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, 3], [3, 0], [9, 8]], "answer": {"point": [7.230769230769231, 3.076923076923077]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, 3), B=(3, 0), C=(9, 8). Find the circumradius.", "im_path": "/images_full/task_06375_circumcircle.png", "im_dots_path": "/images/task_06375_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [7.230769230769231, 3.076923076923077]}, "choices": null, "image_choices": null} | |
| {"qid": 6376, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-4, 8], [-8, -1], [10, 2]], "answer": {"point": [1.02, 0.38]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-4, 8), B=(-8, -1), C=(10, 2). Find the circumradius.", "im_path": "/images_full/task_06376_circumcircle.png", "im_dots_path": "/images/task_06376_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [1.02, 0.38]}, "choices": null, "image_choices": null} | |
| {"qid": 6377, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, -1], [10, -6], [-8, -3]], "answer": {"point": [-0.7222222222222222, -14.833333333333334]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, -1), B=(10, -6), C=(-8, -3). Find the circumradius.", "im_path": "/images_full/task_06377_circumcircle.png", "im_dots_path": "/images/task_06377_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.7222222222222222, -14.833333333333334]}, "choices": null, "image_choices": null} | |
| {"qid": 6378, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[4, 7], [0, -3], [6, -5]], "answer": {"point": [4.647058823529412, 0.9411764705882353]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(4, 7), B=(0, -3), C=(6, -5). Find the circumradius.", "im_path": "/images_full/task_06378_circumcircle.png", "im_dots_path": "/images/task_06378_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [4.647058823529412, 0.9411764705882353]}, "choices": null, "image_choices": null} | |
| {"qid": 6379, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[0, 8], [4, 3], [5, 2]], "answer": {"point": [29.5, 27.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(0, 8), B=(4, 3), C=(5, 2). Find the circumradius.", "im_path": "/images_full/task_06379_circumcircle.png", "im_dots_path": "/images/task_06379_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [29.5, 27.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6380, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[5, -9], [-4, 6], [9, 4]], "answer": {"point": [1.6016949152542372, -0.8389830508474576]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(5, -9), B=(-4, 6), C=(9, 4). Find the circumradius.", "im_path": "/images_full/task_06380_circumcircle.png", "im_dots_path": "/images/task_06380_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [1.6016949152542372, -0.8389830508474576]}, "choices": null, "image_choices": null} | |
| {"qid": 6381, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-3, 3], [-6, 2], [3, -3]], "answer": {"point": [-2.75, -2.75]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-3, 3), B=(-6, 2), C=(3, -3). Find the circumradius.", "im_path": "/images_full/task_06381_circumcircle.png", "im_dots_path": "/images/task_06381_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.75, -2.75]}, "choices": null, "image_choices": null} | |
| {"qid": 6382, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, 5], [-9, -3], [-6, 7]], "answer": {"point": [-5.357142857142857, 1.3571428571428572]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, 5), B=(-9, -3), C=(-6, 7). Find the circumradius.", "im_path": "/images_full/task_06382_circumcircle.png", "im_dots_path": "/images/task_06382_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-5.357142857142857, 1.3571428571428572]}, "choices": null, "image_choices": null} | |
| {"qid": 6383, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[2, -8], [-6, 2], [-2, -9]], "answer": {"point": [-1.4791666666666667, -2.5833333333333335]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(2, -8), B=(-6, 2), C=(-2, -9). Find the circumradius.", "im_path": "/images_full/task_06383_circumcircle.png", "im_dots_path": "/images/task_06383_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.4791666666666667, -2.5833333333333335]}, "choices": null, "image_choices": null} | |
| {"qid": 6384, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[10, 10], [1, -3], [9, 3]], "answer": {"point": [-1.0, 8.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(10, 10), B=(1, -3), C=(9, 3). Find the circumradius.", "im_path": "/images_full/task_06384_circumcircle.png", "im_dots_path": "/images/task_06384_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.0, 8.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6385, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, -6], [5, -1], [5, -4]], "answer": {"point": [0.7857142857142857, -2.5]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, -6), B=(5, -1), C=(5, -4). Find the circumradius.", "im_path": "/images_full/task_06385_circumcircle.png", "im_dots_path": "/images/task_06385_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.7857142857142857, -2.5]}, "choices": null, "image_choices": null} | |
| {"qid": 6386, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[7, 0], [-8, -3], [-5, 8]], "answer": {"point": [-1.0, 1.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(7, 0), B=(-8, -3), C=(-5, 8). Find the circumradius.", "im_path": "/images_full/task_06386_circumcircle.png", "im_dots_path": "/images/task_06386_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-1.0, 1.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6387, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-7, 3], [-3, 5], [6, 10]], "answer": {"point": [-81.0, 156.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-7, 3), B=(-3, 5), C=(6, 10). Find the circumradius.", "im_path": "/images_full/task_06387_circumcircle.png", "im_dots_path": "/images/task_06387_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-81.0, 156.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6388, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-9, 10], [-6, -10], [-1, 8]], "answer": {"point": [-7.240259740259741, 0.03896103896103896]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-9, 10), B=(-6, -10), C=(-1, 8). Find the circumradius.", "im_path": "/images_full/task_06388_circumcircle.png", "im_dots_path": "/images/task_06388_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-7.240259740259741, 0.03896103896103896]}, "choices": null, "image_choices": null} | |
| {"qid": 6389, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, -7], [9, 0], [6, 9]], "answer": {"point": [0.12162162162162163, 2.0405405405405403]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -7), B=(9, 0), C=(6, 9). Find the circumradius.", "im_path": "/images_full/task_06389_circumcircle.png", "im_dots_path": "/images/task_06389_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [0.12162162162162163, 2.0405405405405403]}, "choices": null, "image_choices": null} | |
| {"qid": 6390, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, -8], [-5, 10], [6, -2]], "answer": {"point": [-3.2142857142857144, 0.5952380952380952]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, -8), B=(-5, 10), C=(6, -2). Find the circumradius.", "im_path": "/images_full/task_06390_circumcircle.png", "im_dots_path": "/images/task_06390_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-3.2142857142857144, 0.5952380952380952]}, "choices": null, "image_choices": null} | |
| {"qid": 6391, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-8, 10], [-4, 8], [9, -9]], "answer": {"point": [-18.952380952380953, -16.904761904761905]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-8, 10), B=(-4, 8), C=(9, -9). Find the circumradius.", "im_path": "/images_full/task_06391_circumcircle.png", "im_dots_path": "/images/task_06391_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-18.952380952380953, -16.904761904761905]}, "choices": null, "image_choices": null} | |
| {"qid": 6392, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, -3], [10, -9], [6, 0]], "answer": {"point": [1.7, -7.3]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, -3), B=(10, -9), C=(6, 0). Find the circumradius.", "im_path": "/images_full/task_06392_circumcircle.png", "im_dots_path": "/images/task_06392_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [1.7, -7.3]}, "choices": null, "image_choices": null} | |
| {"qid": 6393, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, -2], [10, 9], [-8, 6]], "answer": {"point": [2.391304347826087, -0.8478260869565217]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, -2), B=(10, 9), C=(-8, 6). Find the circumradius.", "im_path": "/images_full/task_06393_circumcircle.png", "im_dots_path": "/images/task_06393_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [2.391304347826087, -0.8478260869565217]}, "choices": null, "image_choices": null} | |
| {"qid": 6394, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-10, 9], [6, 8], [-9, -7]], "answer": {"point": [-2.4411764705882355, 1.4411764705882353]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-10, 9), B=(6, 8), C=(-9, -7). Find the circumradius.", "im_path": "/images_full/task_06394_circumcircle.png", "im_dots_path": "/images/task_06394_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-2.4411764705882355, 1.4411764705882353]}, "choices": null, "image_choices": null} | |
| {"qid": 6395, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-2, 2], [5, -5], [0, -6]], "answer": {"point": [1.6666666666666667, -1.3333333333333333]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-2, 2), B=(5, -5), C=(0, -6). Find the circumradius.", "im_path": "/images_full/task_06395_circumcircle.png", "im_dots_path": "/images/task_06395_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [1.6666666666666667, -1.3333333333333333]}, "choices": null, "image_choices": null} | |
| {"qid": 6396, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[-1, -8], [3, -5], [-1, -2]], "answer": {"point": [-0.125, -5.0]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(-1, -8), B=(3, -5), C=(-1, -2). Find the circumradius.", "im_path": "/images_full/task_06396_circumcircle.png", "im_dots_path": "/images/task_06396_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [-0.125, -5.0]}, "choices": null, "image_choices": null} | |
| {"qid": 6397, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[9, 5], [-7, -5], [2, 5]], "answer": {"point": [5.5, -7.2]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(9, 5), B=(-7, -5), C=(2, 5). Find the circumradius.", "im_path": "/images_full/task_06397_circumcircle.png", "im_dots_path": "/images/task_06397_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [5.5, -7.2]}, "choices": null, "image_choices": null} | |
| {"qid": 6398, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[1, -6], [3, -8], [-2, 9]], "answer": {"point": [13.25, 4.25]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(1, -6), B=(3, -8), C=(-2, 9). Find the circumradius.", "im_path": "/images_full/task_06398_circumcircle.png", "im_dots_path": "/images/task_06398_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [13.25, 4.25]}, "choices": null, "image_choices": null} | |
| {"qid": 6399, "type": "numeric", "category_id": 63, "category": "Simple circle properties", "difficulty": 2, "schema_type": "point", "points": [[8, -1], [2, 0], [-4, 6]], "answer": {"point": [6.9, 10.9]}, "modality": "image_text", "system_prompt": "You are a highly capable AI assistant with expertise in geometry. You can accurately analyze geometric figures, solve problems.", "question": "Triangle A=(8, -1), B=(2, 0), C=(-4, 6). Find the circumradius.", "im_path": "/images_full/task_06399_circumcircle.png", "im_dots_path": "/images/task_06399_circumcircle.png", "image_system_prompt": "You are a highly capable AI assistant with expertise in visual geometry. You can accurately analyze geometric figures in images, solve problems based on visual input.", "image_question": "Refer to the input image. What is the circumradius?", "image_answer": {"point": [6.9, 10.9]}, "choices": null, "image_choices": null} | |