{"qid": 6100, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[4, -3], [-1, 9], [8, -4]], "answer": 1.3056220052, "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=(-1, 9), C=(8, -4). Find the incircle's radius.", "im_path": "/images_full/task_06100_incircle.png", "im_dots_path": "/images/task_06100_incircle.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 incircle's radius?", "image_answer": 1.3056220052, "choices": null, "image_choices": null}
{"qid": 6101, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, -6], [7, -2], [2, 3]], "answer": 2.5705344447, "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, -2), C=(2, 3). Find the incircle's radius.", "im_path": "/images_full/task_06101_incircle.png", "im_dots_path": "/images/task_06101_incircle.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 incircle's radius?", "image_answer": 2.5705344447, "choices": null, "image_choices": null}
{"qid": 6102, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-3, 1], [5, 3], [-6, 2]], "answer": 0.6235010942, "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=(5, 3), C=(-6, 2). Find the incircle's radius.", "im_path": "/images_full/task_06102_incircle.png", "im_dots_path": "/images/task_06102_incircle.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 incircle's radius?", "image_answer": 0.6235010942, "choices": null, "image_choices": null}
{"qid": 6103, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, 6], [2, -1], [6, -10]], "answer": 1.2659394864, "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=(2, -1), C=(6, -10). Find the incircle's radius.", "im_path": "/images_full/task_06103_incircle.png", "im_dots_path": "/images/task_06103_incircle.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 incircle's radius?", "image_answer": 1.2659394864, "choices": null, "image_choices": null}
{"qid": 6104, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, -4], [7, 10], [2, -3]], "answer": 2.9848137272, "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, -4), B=(7, 10), C=(2, -3). Find the incircle's radius.", "im_path": "/images_full/task_06104_incircle.png", "im_dots_path": "/images/task_06104_incircle.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 incircle's radius?", "image_answer": 2.9848137272, "choices": null, "image_choices": null}
{"qid": 6105, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[5, 5], [10, 9], [-1, 7]], "answer": 1.4221169628, "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=(10, 9), C=(-1, 7). Find the incircle's radius.", "im_path": "/images_full/task_06105_incircle.png", "im_dots_path": "/images/task_06105_incircle.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 incircle's radius?", "image_answer": 1.4221169628, "choices": null, "image_choices": null}
{"qid": 6106, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[9, 9], [-9, -4], [2, 10]], "answer": 2.3152492221, "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, 9), B=(-9, -4), C=(2, 10). Find the incircle's radius.", "im_path": "/images_full/task_06106_incircle.png", "im_dots_path": "/images/task_06106_incircle.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 incircle's radius?", "image_answer": 2.3152492221, "choices": null, "image_choices": null}
{"qid": 6107, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-10, -10], [-9, -5], [-9, 1]], "answer": 0.2709491011, "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=(-9, -5), C=(-9, 1). Find the incircle's radius.", "im_path": "/images_full/task_06107_incircle.png", "im_dots_path": "/images/task_06107_incircle.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 incircle's radius?", "image_answer": 0.2709491011, "choices": null, "image_choices": null}
{"qid": 6108, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[3, -8], [0, -3], [-10, -4]], "answer": 1.7976889032, "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, -8), B=(0, -3), C=(-10, -4). Find the incircle's radius.", "im_path": "/images_full/task_06108_incircle.png", "im_dots_path": "/images/task_06108_incircle.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 incircle's radius?", "image_answer": 1.7976889032, "choices": null, "image_choices": null}
{"qid": 6109, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[10, 9], [3, 7], [-8, 9]], "answer": 0.9873712535, "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=(3, 7), C=(-8, 9). Find the incircle's radius.", "im_path": "/images_full/task_06109_incircle.png", "im_dots_path": "/images/task_06109_incircle.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 incircle's radius?", "image_answer": 0.9873712535, "choices": null, "image_choices": null}
{"qid": 6110, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-3, -6], [6, 7], [5, -7]], "answer": 2.9807977355, "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=(6, 7), C=(5, -7). Find the incircle's radius.", "im_path": "/images_full/task_06110_incircle.png", "im_dots_path": "/images/task_06110_incircle.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 incircle's radius?", "image_answer": 2.9807977355, "choices": null, "image_choices": null}
{"qid": 6111, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[3, -5], [-2, -4], [-9, 8]], "answer": 1.4448003327, "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, -5), B=(-2, -4), C=(-9, 8). Find the incircle's radius.", "im_path": "/images_full/task_06111_incircle.png", "im_dots_path": "/images/task_06111_incircle.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 incircle's radius?", "image_answer": 1.4448003327, "choices": null, "image_choices": null}
{"qid": 6112, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-1, -4], [-8, 6], [2, 7]], "answer": 3.1790186681, "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=(-8, 6), C=(2, 7). Find the incircle's radius.", "im_path": "/images_full/task_06112_incircle.png", "im_dots_path": "/images/task_06112_incircle.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 incircle's radius?", "image_answer": 3.1790186681, "choices": null, "image_choices": null}
{"qid": 6113, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[1, -10], [-7, 1], [-9, 4]], "answer": 0.0581198142, "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, -10), B=(-7, 1), C=(-9, 4). Find the incircle's radius.", "im_path": "/images_full/task_06113_incircle.png", "im_dots_path": "/images/task_06113_incircle.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 incircle's radius?", "image_answer": 0.0581198142, "choices": null, "image_choices": null}
{"qid": 6114, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-4, 9], [9, -2], [2, 5]], "answer": 0.4100763509, "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, 9), B=(9, -2), C=(2, 5). Find the incircle's radius.", "im_path": "/images_full/task_06114_incircle.png", "im_dots_path": "/images/task_06114_incircle.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 incircle's radius?", "image_answer": 0.4100763509, "choices": null, "image_choices": null}
{"qid": 6115, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, 6], [-8, -3], [-7, -3]], "answer": 0.4723074309, "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, -3), C=(-7, -3). Find the incircle's radius.", "im_path": "/images_full/task_06115_incircle.png", "im_dots_path": "/images/task_06115_incircle.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 incircle's radius?", "image_answer": 0.4723074309, "choices": null, "image_choices": null}
{"qid": 6116, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-1, 4], [1, 6], [9, 7]], "answer": 0.6563220504, "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=(1, 6), C=(9, 7). Find the incircle's radius.", "im_path": "/images_full/task_06116_incircle.png", "im_dots_path": "/images/task_06116_incircle.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 incircle's radius?", "image_answer": 0.6563220504, "choices": null, "image_choices": null}
{"qid": 6117, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[10, 1], [6, 0], [-10, -6]], "answer": 0.1886759825, "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=(6, 0), C=(-10, -6). Find the incircle's radius.", "im_path": "/images_full/task_06117_incircle.png", "im_dots_path": "/images/task_06117_incircle.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 incircle's radius?", "image_answer": 0.1886759825, "choices": null, "image_choices": null}
{"qid": 6118, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, -3], [-3, 8], [-1, 0]], "answer": 1.5556842136, "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=(-3, 8), C=(-1, 0). Find the incircle's radius.", "im_path": "/images_full/task_06118_incircle.png", "im_dots_path": "/images/task_06118_incircle.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 incircle's radius?", "image_answer": 1.5556842136, "choices": null, "image_choices": null}
{"qid": 6119, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[2, 5], [9, -9], [-10, 0]], "answer": 4.0864580272, "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, 5), B=(9, -9), C=(-10, 0). Find the incircle's radius.", "im_path": "/images_full/task_06119_incircle.png", "im_dots_path": "/images/task_06119_incircle.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 incircle's radius?", "image_answer": 4.0864580272, "choices": null, "image_choices": null}
{"qid": 6120, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, 7], [8, 7], [6, 1]], "answer": 2.5250841591, "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, 7), B=(8, 7), C=(6, 1). Find the incircle's radius.", "im_path": "/images_full/task_06120_incircle.png", "im_dots_path": "/images/task_06120_incircle.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 incircle's radius?", "image_answer": 2.5250841591, "choices": null, "image_choices": null}
{"qid": 6121, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-4, -1], [3, 6], [-1, 8]], "answer": 1.7603815663, "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, -1), B=(3, 6), C=(-1, 8). Find the incircle's radius.", "im_path": "/images_full/task_06121_incircle.png", "im_dots_path": "/images/task_06121_incircle.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 incircle's radius?", "image_answer": 1.7603815663, "choices": null, "image_choices": null}
{"qid": 6122, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[8, -9], [0, -6], [3, 3]], "answer": 2.6103066674, "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=(0, -6), C=(3, 3). Find the incircle's radius.", "im_path": "/images_full/task_06122_incircle.png", "im_dots_path": "/images/task_06122_incircle.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 incircle's radius?", "image_answer": 2.6103066674, "choices": null, "image_choices": null}
{"qid": 6123, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[9, -6], [9, 7], [7, 4]], "answer": 0.9700193036, "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=(9, 7), C=(7, 4). Find the incircle's radius.", "im_path": "/images_full/task_06123_incircle.png", "im_dots_path": "/images/task_06123_incircle.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 incircle's radius?", "image_answer": 0.9700193036, "choices": null, "image_choices": null}
{"qid": 6124, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[0, -1], [5, -10], [5, 7]], "answer": 2.3142090824, "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, -1), B=(5, -10), C=(5, 7). Find the incircle's radius.", "im_path": "/images_full/task_06124_incircle.png", "im_dots_path": "/images/task_06124_incircle.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 incircle's radius?", "image_answer": 2.3142090824, "choices": null, "image_choices": null}
{"qid": 6125, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, -9], [-8, 8], [9, -5]], "answer": 4.1264621122, "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=(-8, 8), C=(9, -5). Find the incircle's radius.", "im_path": "/images_full/task_06125_incircle.png", "im_dots_path": "/images/task_06125_incircle.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 incircle's radius?", "image_answer": 4.1264621122, "choices": null, "image_choices": null}
{"qid": 6126, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, -3], [6, 2], [-7, 5]], "answer": 2.910523272, "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=(6, 2), C=(-7, 5). Find the incircle's radius.", "im_path": "/images_full/task_06126_incircle.png", "im_dots_path": "/images/task_06126_incircle.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 incircle's radius?", "image_answer": 2.910523272, "choices": null, "image_choices": null}
{"qid": 6127, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, 7], [-8, -7], [-3, -6]], "answer": 1.9179494894, "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, 7), B=(-8, -7), C=(-3, -6). Find the incircle's radius.", "im_path": "/images_full/task_06127_incircle.png", "im_dots_path": "/images/task_06127_incircle.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 incircle's radius?", "image_answer": 1.9179494894, "choices": null, "image_choices": null}
{"qid": 6128, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-4, 3], [-7, 7], [-8, -4]], "answer": 1.534784516, "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=(-7, 7), C=(-8, -4). Find the incircle's radius.", "im_path": "/images_full/task_06128_incircle.png", "im_dots_path": "/images/task_06128_incircle.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 incircle's radius?", "image_answer": 1.534784516, "choices": null, "image_choices": null}
{"qid": 6129, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-10, -3], [9, 8], [6, 6]], "answer": 0.1138495484, "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, -3), B=(9, 8), C=(6, 6). Find the incircle's radius.", "im_path": "/images_full/task_06129_incircle.png", "im_dots_path": "/images/task_06129_incircle.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 incircle's radius?", "image_answer": 0.1138495484, "choices": null, "image_choices": null}
{"qid": 6130, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[8, -8], [-4, 5], [-3, 7]], "answer": 0.9603168719, "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, -8), B=(-4, 5), C=(-3, 7). Find the incircle's radius.", "im_path": "/images_full/task_06130_incircle.png", "im_dots_path": "/images/task_06130_incircle.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 incircle's radius?", "image_answer": 0.9603168719, "choices": null, "image_choices": null}
{"qid": 6131, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[4, -1], [-4, -8], [1, 3]], "answer": 1.9124466214, "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, -1), B=(-4, -8), C=(1, 3). Find the incircle's radius.", "im_path": "/images_full/task_06131_incircle.png", "im_dots_path": "/images/task_06131_incircle.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 incircle's radius?", "image_answer": 1.9124466214, "choices": null, "image_choices": null}
{"qid": 6132, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, -8], [8, 0], [1, 10]], "answer": 4.2123110081, "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=(8, 0), C=(1, 10). Find the incircle's radius.", "im_path": "/images_full/task_06132_incircle.png", "im_dots_path": "/images/task_06132_incircle.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 incircle's radius?", "image_answer": 4.2123110081, "choices": null, "image_choices": null}
{"qid": 6133, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-4, -6], [-10, 7], [-6, -4]], "answer": 0.485252684, "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=(-10, 7), C=(-6, -4). Find the incircle's radius.", "im_path": "/images_full/task_06133_incircle.png", "im_dots_path": "/images/task_06133_incircle.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 incircle's radius?", "image_answer": 0.485252684, "choices": null, "image_choices": null}
{"qid": 6134, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[0, -2], [-2, 9], [7, 1]], "answer": 2.6915100549, "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=(-2, 9), C=(7, 1). Find the incircle's radius.", "im_path": "/images_full/task_06134_incircle.png", "im_dots_path": "/images/task_06134_incircle.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 incircle's radius?", "image_answer": 2.6915100549, "choices": null, "image_choices": null}
{"qid": 6135, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-10, -3], [-5, 9], [7, 5]], "answer": 3.6905845534, "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, -3), B=(-5, 9), C=(7, 5). Find the incircle's radius.", "im_path": "/images_full/task_06135_incircle.png", "im_dots_path": "/images/task_06135_incircle.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 incircle's radius?", "image_answer": 3.6905845534, "choices": null, "image_choices": null}
{"qid": 6136, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[2, -6], [-2, 4], [-1, 1]], "answer": 0.0928144002, "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=(-2, 4), C=(-1, 1). Find the incircle's radius.", "im_path": "/images_full/task_06136_incircle.png", "im_dots_path": "/images/task_06136_incircle.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 incircle's radius?", "image_answer": 0.0928144002, "choices": null, "image_choices": null}
{"qid": 6137, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-3, 5], [1, -9], [-7, 5]], "answer": 1.6145430996, "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, 5), B=(1, -9), C=(-7, 5). Find the incircle's radius.", "im_path": "/images_full/task_06137_incircle.png", "im_dots_path": "/images/task_06137_incircle.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 incircle's radius?", "image_answer": 1.6145430996, "choices": null, "image_choices": null}
{"qid": 6138, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-10, 7], [-2, 8], [0, -8]], "answer": 3.0795084338, "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, 7), B=(-2, 8), C=(0, -8). Find the incircle's radius.", "im_path": "/images_full/task_06138_incircle.png", "im_dots_path": "/images/task_06138_incircle.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 incircle's radius?", "image_answer": 3.0795084338, "choices": null, "image_choices": null}
{"qid": 6139, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[10, -6], [-4, -9], [1, -3]], "answer": 2.1825149497, "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, -6), B=(-4, -9), C=(1, -3). Find the incircle's radius.", "im_path": "/images_full/task_06139_incircle.png", "im_dots_path": "/images/task_06139_incircle.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 incircle's radius?", "image_answer": 2.1825149497, "choices": null, "image_choices": null}
{"qid": 6140, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[6, -3], [8, -5], [9, 0]], "answer": 0.9860241491, "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=(8, -5), C=(9, 0). Find the incircle's radius.", "im_path": "/images_full/task_06140_incircle.png", "im_dots_path": "/images/task_06140_incircle.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 incircle's radius?", "image_answer": 0.9860241491, "choices": null, "image_choices": null}
{"qid": 6141, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, 5], [-8, 6], [1, 10]], "answer": 1.5163648697, "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, 5), B=(-8, 6), C=(1, 10). Find the incircle's radius.", "im_path": "/images_full/task_06141_incircle.png", "im_dots_path": "/images/task_06141_incircle.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 incircle's radius?", "image_answer": 1.5163648697, "choices": null, "image_choices": null}
{"qid": 6142, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-6, -6], [-1, -1], [-10, -5]], "answer": 1.1880417662, "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, -6), B=(-1, -1), C=(-10, -5). Find the incircle's radius.", "im_path": "/images_full/task_06142_incircle.png", "im_dots_path": "/images/task_06142_incircle.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 incircle's radius?", "image_answer": 1.1880417662, "choices": null, "image_choices": null}
{"qid": 6143, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[9, -8], [7, 3], [0, 10]], "answer": 1.5289611963, "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=(7, 3), C=(0, 10). Find the incircle's radius.", "im_path": "/images_full/task_06143_incircle.png", "im_dots_path": "/images/task_06143_incircle.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 incircle's radius?", "image_answer": 1.5289611963, "choices": null, "image_choices": null}
{"qid": 6144, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[9, -9], [-10, 5], [0, 2]], "answer": 1.7200709189, "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, -9), B=(-10, 5), C=(0, 2). Find the incircle's radius.", "im_path": "/images_full/task_06144_incircle.png", "im_dots_path": "/images/task_06144_incircle.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 incircle's radius?", "image_answer": 1.7200709189, "choices": null, "image_choices": null}
{"qid": 6145, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, -5], [-9, -6], [-5, -3]], "answer": 0.7192235936, "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=(-9, -6), C=(-5, -3). Find the incircle's radius.", "im_path": "/images_full/task_06145_incircle.png", "im_dots_path": "/images/task_06145_incircle.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 incircle's radius?", "image_answer": 0.7192235936, "choices": null, "image_choices": null}
{"qid": 6146, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, 7], [-2, 3], [-3, 5]], "answer": 0.6015804344, "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=(-2, 3), C=(-3, 5). Find the incircle's radius.", "im_path": "/images_full/task_06146_incircle.png", "im_dots_path": "/images/task_06146_incircle.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 incircle's radius?", "image_answer": 0.6015804344, "choices": null, "image_choices": null}
{"qid": 6147, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, 0], [-4, -2], [9, -4]], "answer": 0.4326990667, "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=(-4, -2), C=(9, -4). Find the incircle's radius.", "im_path": "/images_full/task_06147_incircle.png", "im_dots_path": "/images/task_06147_incircle.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 incircle's radius?", "image_answer": 0.4326990667, "choices": null, "image_choices": null}
{"qid": 6148, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, 9], [10, -6], [-7, 1]], "answer": 3.1351768495, "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=(10, -6), C=(-7, 1). Find the incircle's radius.", "im_path": "/images_full/task_06148_incircle.png", "im_dots_path": "/images/task_06148_incircle.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 incircle's radius?", "image_answer": 3.1351768495, "choices": null, "image_choices": null}
{"qid": 6149, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-4, 1], [-8, 8], [10, 7]], "answer": 2.9524538523, "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, 1), B=(-8, 8), C=(10, 7). Find the incircle's radius.", "im_path": "/images_full/task_06149_incircle.png", "im_dots_path": "/images/task_06149_incircle.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 incircle's radius?", "image_answer": 2.9524538523, "choices": null, "image_choices": null}
{"qid": 6150, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, -3], [2, -3], [-6, 2]], "answer": 1.9122083358, "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=(2, -3), C=(-6, 2). Find the incircle's radius.", "im_path": "/images_full/task_06150_incircle.png", "im_dots_path": "/images/task_06150_incircle.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 incircle's radius?", "image_answer": 1.9122083358, "choices": null, "image_choices": null}
{"qid": 6151, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[2, -7], [3, -6], [-1, -6]], "answer": 0.4663911961, "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, -7), B=(3, -6), C=(-1, -6). Find the incircle's radius.", "im_path": "/images_full/task_06151_incircle.png", "im_dots_path": "/images/task_06151_incircle.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 incircle's radius?", "image_answer": 0.4663911961, "choices": null, "image_choices": null}
{"qid": 6152, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, 5], [9, -5], [-7, 10]], "answer": 2.2960608829, "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=(9, -5), C=(-7, 10). Find the incircle's radius.", "im_path": "/images_full/task_06152_incircle.png", "im_dots_path": "/images/task_06152_incircle.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 incircle's radius?", "image_answer": 2.2960608829, "choices": null, "image_choices": null}
{"qid": 6153, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-6, 1], [-2, -9], [-1, -4]], "answer": 1.3077356039, "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, 1), B=(-2, -9), C=(-1, -4). Find the incircle's radius.", "im_path": "/images_full/task_06153_incircle.png", "im_dots_path": "/images/task_06153_incircle.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 incircle's radius?", "image_answer": 1.3077356039, "choices": null, "image_choices": null}
{"qid": 6154, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, 9], [8, -2], [-1, -8]], "answer": 3.7225977351, "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=(8, -2), C=(-1, -8). Find the incircle's radius.", "im_path": "/images_full/task_06154_incircle.png", "im_dots_path": "/images/task_06154_incircle.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 incircle's radius?", "image_answer": 3.7225977351, "choices": null, "image_choices": null}
{"qid": 6155, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-1, 0], [4, 1], [-6, 5]], "answer": 1.3077356039, "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=(4, 1), C=(-6, 5). Find the incircle's radius.", "im_path": "/images_full/task_06155_incircle.png", "im_dots_path": "/images/task_06155_incircle.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 incircle's radius?", "image_answer": 1.3077356039, "choices": null, "image_choices": null}
{"qid": 6156, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[9, 6], [5, 2], [-9, -1]], "answer": 1.1199381688, "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=(5, 2), C=(-9, -1). Find the incircle's radius.", "im_path": "/images_full/task_06156_incircle.png", "im_dots_path": "/images/task_06156_incircle.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 incircle's radius?", "image_answer": 1.1199381688, "choices": null, "image_choices": null}
{"qid": 6157, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-10, 9], [-7, -2], [5, -3]], "answer": 3.0244259999, "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=(-7, -2), C=(5, -3). Find the incircle's radius.", "im_path": "/images_full/task_06157_incircle.png", "im_dots_path": "/images/task_06157_incircle.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 incircle's radius?", "image_answer": 3.0244259999, "choices": null, "image_choices": null}
{"qid": 6158, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[7, -7], [8, 7], [-4, -1]], "answer": 3.9035969612, "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, -7), B=(8, 7), C=(-4, -1). Find the incircle's radius.", "im_path": "/images_full/task_06158_incircle.png", "im_dots_path": "/images/task_06158_incircle.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 incircle's radius?", "image_answer": 3.9035969612, "choices": null, "image_choices": null}
{"qid": 6159, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[5, -7], [-10, -5], [4, -3]], "answer": 1.7366316016, "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, -7), B=(-10, -5), C=(4, -3). Find the incircle's radius.", "im_path": "/images_full/task_06159_incircle.png", "im_dots_path": "/images/task_06159_incircle.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 incircle's radius?", "image_answer": 1.7366316016, "choices": null, "image_choices": null}
{"qid": 6160, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[7, -2], [-2, 2], [7, 0]], "answer": 0.8543599927, "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=(-2, 2), C=(7, 0). Find the incircle's radius.", "im_path": "/images_full/task_06160_incircle.png", "im_dots_path": "/images/task_06160_incircle.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 incircle's radius?", "image_answer": 0.8543599927, "choices": null, "image_choices": null}
{"qid": 6161, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, -1], [-9, -2], [5, -3]], "answer": 0.6347680779, "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, -1), B=(-9, -2), C=(5, -3). Find the incircle's radius.", "im_path": "/images_full/task_06161_incircle.png", "im_dots_path": "/images/task_06161_incircle.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 incircle's radius?", "image_answer": 0.6347680779, "choices": null, "image_choices": null}
{"qid": 6162, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, -7], [-10, -9], [-4, 5]], "answer": 0.9613408208, "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, -7), B=(-10, -9), C=(-4, 5). Find the incircle's radius.", "im_path": "/images_full/task_06162_incircle.png", "im_dots_path": "/images/task_06162_incircle.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 incircle's radius?", "image_answer": 0.9613408208, "choices": null, "image_choices": null}
{"qid": 6163, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[7, 5], [1, -4], [-1, 10]], "answer": 2.9657395515, "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=(1, -4), C=(-1, 10). Find the incircle's radius.", "im_path": "/images_full/task_06163_incircle.png", "im_dots_path": "/images/task_06163_incircle.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 incircle's radius?", "image_answer": 2.9657395515, "choices": null, "image_choices": null}
{"qid": 6164, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[6, 6], [-6, 6], [1, -6]], "answer": 3.7025186702, "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, 6), B=(-6, 6), C=(1, -6). Find the incircle's radius.", "im_path": "/images_full/task_06164_incircle.png", "im_dots_path": "/images/task_06164_incircle.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 incircle's radius?", "image_answer": 3.7025186702, "choices": null, "image_choices": null}
{"qid": 6165, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, 8], [-10, 5], [0, -5]], "answer": 1.2078825843, "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=(0, -5). Find the incircle's radius.", "im_path": "/images_full/task_06165_incircle.png", "im_dots_path": "/images/task_06165_incircle.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 incircle's radius?", "image_answer": 1.2078825843, "choices": null, "image_choices": null}
{"qid": 6166, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[6, -8], [-5, -4], [-5, -10]], "answer": 2.2849198222, "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=(-5, -4), C=(-5, -10). Find the incircle's radius.", "im_path": "/images_full/task_06166_incircle.png", "im_dots_path": "/images/task_06166_incircle.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 incircle's radius?", "image_answer": 2.2849198222, "choices": null, "image_choices": null}
{"qid": 6167, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, -6], [4, 4], [-3, -3]], "answer": 0.6361917039, "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=(4, 4), C=(-3, -3). Find the incircle's radius.", "im_path": "/images_full/task_06167_incircle.png", "im_dots_path": "/images/task_06167_incircle.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 incircle's radius?", "image_answer": 0.6361917039, "choices": null, "image_choices": null}
{"qid": 6168, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[3, 4], [-10, -6], [5, 3]], "answer": 0.9133647736, "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, 4), B=(-10, -6), C=(5, 3). Find the incircle's radius.", "im_path": "/images_full/task_06168_incircle.png", "im_dots_path": "/images/task_06168_incircle.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 incircle's radius?", "image_answer": 0.9133647736, "choices": null, "image_choices": null}
{"qid": 6169, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[10, -6], [2, 0], [-2, 2]], "answer": 0.2768708234, "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, -6), B=(2, 0), C=(-2, 2). Find the incircle's radius.", "im_path": "/images_full/task_06169_incircle.png", "im_dots_path": "/images/task_06169_incircle.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 incircle's radius?", "image_answer": 0.2768708234, "choices": null, "image_choices": null}
{"qid": 6170, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[3, -8], [-4, -10], [-8, -7]], "answer": 1.2432760786, "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, -8), B=(-4, -10), C=(-8, -7). Find the incircle's radius.", "im_path": "/images_full/task_06170_incircle.png", "im_dots_path": "/images/task_06170_incircle.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 incircle's radius?", "image_answer": 1.2432760786, "choices": null, "image_choices": null}
{"qid": 6171, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, -4], [-9, -10], [3, 0]], "answer": 2.1009868515, "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, -4), B=(-9, -10), C=(3, 0). Find the incircle's radius.", "im_path": "/images_full/task_06171_incircle.png", "im_dots_path": "/images/task_06171_incircle.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 incircle's radius?", "image_answer": 2.1009868515, "choices": null, "image_choices": null}
{"qid": 6172, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, 2], [5, 2], [-2, -5]], "answer": 2.0502525317, "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, 2), C=(-2, -5). Find the incircle's radius.", "im_path": "/images_full/task_06172_incircle.png", "im_dots_path": "/images/task_06172_incircle.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 incircle's radius?", "image_answer": 2.0502525317, "choices": null, "image_choices": null}
{"qid": 6173, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-10, -6], [1, 8], [2, -8]], "answer": 4.1303235856, "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, -6), B=(1, 8), C=(2, -8). Find the incircle's radius.", "im_path": "/images_full/task_06173_incircle.png", "im_dots_path": "/images/task_06173_incircle.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 incircle's radius?", "image_answer": 4.1303235856, "choices": null, "image_choices": null}
{"qid": 6174, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, -1], [-10, 9], [8, -10]], "answer": 2.9031101761, "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=(-10, 9), C=(8, -10). Find the incircle's radius.", "im_path": "/images_full/task_06174_incircle.png", "im_dots_path": "/images/task_06174_incircle.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 incircle's radius?", "image_answer": 2.9031101761, "choices": null, "image_choices": null}
{"qid": 6175, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, -2], [1, 4], [0, 0]], "answer": 0.4392471202, "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=(1, 4), C=(0, 0). Find the incircle's radius.", "im_path": "/images_full/task_06175_incircle.png", "im_dots_path": "/images/task_06175_incircle.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 incircle's radius?", "image_answer": 0.4392471202, "choices": null, "image_choices": null}
{"qid": 6176, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-9, 8], [-6, 4], [3, 10]], "answer": 1.9297996849, "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=(-6, 4), C=(3, 10). Find the incircle's radius.", "im_path": "/images_full/task_06176_incircle.png", "im_dots_path": "/images/task_06176_incircle.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 incircle's radius?", "image_answer": 1.9297996849, "choices": null, "image_choices": null}
{"qid": 6177, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[5, 9], [4, 2], [4, -5]], "answer": 0.2490506132, "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, 2), C=(4, -5). Find the incircle's radius.", "im_path": "/images_full/task_06177_incircle.png", "im_dots_path": "/images/task_06177_incircle.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 incircle's radius?", "image_answer": 0.2490506132, "choices": null, "image_choices": null}
{"qid": 6178, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[1, 10], [-10, -10], [-2, -6]], "answer": 2.4142264407, "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, 10), B=(-10, -10), C=(-2, -6). Find the incircle's radius.", "im_path": "/images_full/task_06178_incircle.png", "im_dots_path": "/images/task_06178_incircle.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 incircle's radius?", "image_answer": 2.4142264407, "choices": null, "image_choices": null}
{"qid": 6179, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-4, 6], [-8, 4], [-7, 0]], "answer": 1.1762057103, "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=(-8, 4), C=(-7, 0). Find the incircle's radius.", "im_path": "/images_full/task_06179_incircle.png", "im_dots_path": "/images/task_06179_incircle.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 incircle's radius?", "image_answer": 1.1762057103, "choices": null, "image_choices": null}
{"qid": 6180, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[4, 7], [2, 5], [8, -10]], "answer": 1.1523212042, "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=(2, 5), C=(8, -10). Find the incircle's radius.", "im_path": "/images_full/task_06180_incircle.png", "im_dots_path": "/images/task_06180_incircle.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 incircle's radius?", "image_answer": 1.1523212042, "choices": null, "image_choices": null}
{"qid": 6181, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-6, 5], [1, -1], [-7, 9]], "answer": 0.8413356284, "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=(1, -1), C=(-7, 9). Find the incircle's radius.", "im_path": "/images_full/task_06181_incircle.png", "im_dots_path": "/images/task_06181_incircle.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 incircle's radius?", "image_answer": 0.8413356284, "choices": null, "image_choices": null}
{"qid": 6182, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[10, 1], [-5, -2], [10, 0]], "answer": 0.4772540028, "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, -2), C=(10, 0). Find the incircle's radius.", "im_path": "/images_full/task_06182_incircle.png", "im_dots_path": "/images/task_06182_incircle.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 incircle's radius?", "image_answer": 0.4772540028, "choices": null, "image_choices": null}
{"qid": 6183, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-3, -2], [6, 7], [-2, 1]], "answer": 0.6952437677, "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, -2), B=(6, 7), C=(-2, 1). Find the incircle's radius.", "im_path": "/images_full/task_06183_incircle.png", "im_dots_path": "/images/task_06183_incircle.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 incircle's radius?", "image_answer": 0.6952437677, "choices": null, "image_choices": null}
{"qid": 6184, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[5, -10], [7, -9], [-9, -3]], "answer": 0.8005363294, "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, -10), B=(7, -9), C=(-9, -3). Find the incircle's radius.", "im_path": "/images_full/task_06184_incircle.png", "im_dots_path": "/images/task_06184_incircle.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 incircle's radius?", "image_answer": 0.8005363294, "choices": null, "image_choices": null}
{"qid": 6185, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[1, 0], [-10, -4], [-1, 8]], "answer": 2.7467095079, "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=(-10, -4), C=(-1, 8). Find the incircle's radius.", "im_path": "/images_full/task_06185_incircle.png", "im_dots_path": "/images/task_06185_incircle.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 incircle's radius?", "image_answer": 2.7467095079, "choices": null, "image_choices": null}
{"qid": 6186, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[0, -8], [-2, -6], [0, -4]], "answer": 0.8284271247, "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=(-2, -6), C=(0, -4). Find the incircle's radius.", "im_path": "/images_full/task_06186_incircle.png", "im_dots_path": "/images/task_06186_incircle.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 incircle's radius?", "image_answer": 0.8284271247, "choices": null, "image_choices": null}
{"qid": 6187, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[3, -5], [5, 2], [1, 3]], "answer": 1.5267620963, "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, -5), B=(5, 2), C=(1, 3). Find the incircle's radius.", "im_path": "/images_full/task_06187_incircle.png", "im_dots_path": "/images/task_06187_incircle.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 incircle's radius?", "image_answer": 1.5267620963, "choices": null, "image_choices": null}
{"qid": 6188, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-6, 10], [-7, -9], [-7, 6]], "answer": 0.3931909476, "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, -9), C=(-7, 6). Find the incircle's radius.", "im_path": "/images_full/task_06188_incircle.png", "im_dots_path": "/images/task_06188_incircle.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 incircle's radius?", "image_answer": 0.3931909476, "choices": null, "image_choices": null}
{"qid": 6189, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-6, 5], [5, 10], [1, -9]], "answer": 4.0083127184, "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=(1, -9). Find the incircle's radius.", "im_path": "/images_full/task_06189_incircle.png", "im_dots_path": "/images/task_06189_incircle.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 incircle's radius?", "image_answer": 4.0083127184, "choices": null, "image_choices": null}
{"qid": 6190, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-2, 7], [-4, -4], [3, -6]], "answer": 2.5008615581, "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, 7), B=(-4, -4), C=(3, -6). Find the incircle's radius.", "im_path": "/images_full/task_06190_incircle.png", "im_dots_path": "/images/task_06190_incircle.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 incircle's radius?", "image_answer": 2.5008615581, "choices": null, "image_choices": null}
{"qid": 6191, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[2, 5], [5, 4], [-9, 1]], "answer": 0.7880815039, "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, 5), B=(5, 4), C=(-9, 1). Find the incircle's radius.", "im_path": "/images_full/task_06191_incircle.png", "im_dots_path": "/images/task_06191_incircle.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 incircle's radius?", "image_answer": 0.7880815039, "choices": null, "image_choices": null}
{"qid": 6192, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, 9], [0, 3], [6, -6]], "answer": 0.676935502, "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, 9), B=(0, 3), C=(6, -6). Find the incircle's radius.", "im_path": "/images_full/task_06192_incircle.png", "im_dots_path": "/images/task_06192_incircle.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 incircle's radius?", "image_answer": 0.676935502, "choices": null, "image_choices": null}
{"qid": 6193, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[5, 7], [10, -6], [0, 6]], "answer": 2.0203240476, "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, 7), B=(10, -6), C=(0, 6). Find the incircle's radius.", "im_path": "/images_full/task_06193_incircle.png", "im_dots_path": "/images/task_06193_incircle.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 incircle's radius?", "image_answer": 2.0203240476, "choices": null, "image_choices": null}
{"qid": 6194, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[9, 3], [1, -6], [-3, 7]], "answer": 3.6560993816, "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, -6), C=(-3, 7). Find the incircle's radius.", "im_path": "/images_full/task_06194_incircle.png", "im_dots_path": "/images/task_06194_incircle.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 incircle's radius?", "image_answer": 3.6560993816, "choices": null, "image_choices": null}
{"qid": 6195, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[6, 5], [2, -10], [9, 3]], "answer": 1.5636732606, "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=(2, -10), C=(9, 3). Find the incircle's radius.", "im_path": "/images_full/task_06195_incircle.png", "im_dots_path": "/images/task_06195_incircle.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 incircle's radius?", "image_answer": 1.5636732606, "choices": null, "image_choices": null}
{"qid": 6196, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-7, 9], [6, 4], [-4, 2]], "answer": 2.3942889597, "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, 9), B=(6, 4), C=(-4, 2). Find the incircle's radius.", "im_path": "/images_full/task_06196_incircle.png", "im_dots_path": "/images/task_06196_incircle.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 incircle's radius?", "image_answer": 2.3942889597, "choices": null, "image_choices": null}
{"qid": 6197, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-5, 10], [8, 2], [9, 2]], "answer": 0.2469985583, "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, 10), B=(8, 2), C=(9, 2). Find the incircle's radius.", "im_path": "/images_full/task_06197_incircle.png", "im_dots_path": "/images/task_06197_incircle.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 incircle's radius?", "image_answer": 0.2469985583, "choices": null, "image_choices": null}
{"qid": 6198, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[-3, 8], [2, -3], [-2, 4]], "answer": 0.3708524886, "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, 8), B=(2, -3), C=(-2, 4). Find the incircle's radius.", "im_path": "/images_full/task_06198_incircle.png", "im_dots_path": "/images/task_06198_incircle.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 incircle's radius?", "image_answer": 0.3708524886, "choices": null, "image_choices": null}
{"qid": 6199, "type": "numeric", "category_id": 61, "category": "Simple circle properties", "difficulty": 2, "schema_type": "number", "points": [[6, -7], [-2, 10], [-8, -3]], "answer": 4.321708386, "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, 10), C=(-8, -3). Find the incircle's radius.", "im_path": "/images_full/task_06199_incircle.png", "im_dots_path": "/images/task_06199_incircle.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 incircle's radius?", "image_answer": 4.321708386, "choices": null, "image_choices": null}