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jamescai20
/
tts-reasoning

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dict
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, -1), B=(-1, 3), and C=(-4, 7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.333", "style": "rule" }
{ "index": 1100, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(10, 10), B=(-4, 0), and C=(2, 1), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "26.08°", "style": "rule" }
{ "index": 1101, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(5, 5), B=(5, -5), and C=(7, -6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "116.57°", "style": "rule" }
{ "index": 1102, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(8, -1), B=(8, 0), and C=(-5, 0). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.481", "style": "rule" }
{ "index": 1103, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(4, 5), B=(-8, 1), and C=(3, 2), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "13.24°", "style": "rule" }
{ "index": 1104, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(4, -2), B=(6, 1), and C=(-9, 6). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.586", "style": "rule" }
{ "index": 1105, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(1, 7), B=(-5, 2), and C=(6, 6), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-2.226, 15.871)", "style": "rule" }
{ "index": 1106, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-3, 1), B=(0, 5), and C=(0, -2), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "36.87°", "style": "rule" }
{ "index": 1107, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(3, 7), B=(-7, -3), and C=(-10, -3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.894", "style": "rule" }
{ "index": 1108, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(9, -4), B=(-2, 3), and C=(6, -5). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.163", "style": "rule" }
{ "index": 1109, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(8, 9), B=(-8, 0), and C=(5, -9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "64.05°", "style": "rule" }
{ "index": 1110, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(3, 9), B=(3, -3), and C=(5, 7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.959", "style": "rule" }
{ "index": 1111, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-10, -7), B=(10, 3), and C=(6, 10), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "86.82°", "style": "rule" }
{ "index": 1112, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(7, -1), B=(-4, -3), and C=(-8, -10). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.878", "style": "rule" }
{ "index": 1113, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-7, 2), B=(1, 3), and C=(4, 3), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "172.87°", "style": "rule" }
{ "index": 1114, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(2, -4), B=(-8, 5), and C=(9, 9), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "55.23°", "style": "rule" }
{ "index": 1115, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-8, -8), B=(3, -2), and C=(1, -4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(16.600, -32.600)", "style": "rule" }
{ "index": 1116, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(2, 10), B=(5, -4), and C=(0, 9). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.017", "style": "rule" }
{ "index": 1117, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-3, 4), B=(2, 5), and C=(8, 1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(5.000, 16.000)", "style": "rule" }
{ "index": 1118, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(1, 8), B=(-9, -6), and C=(5, -6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "54.46°", "style": "rule" }
{ "index": 1119, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-9, -10), B=(-1, -8), and C=(-4, 2), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-1.558, -7.767)", "style": "rule" }
{ "index": 1120, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-5, 4), B=(3, -8), and C=(-1, -9). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.742", "style": "rule" }
{ "index": 1121, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-3, -6), B=(-7, -1), and C=(-10, -4). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.506", "style": "rule" }
{ "index": 1122, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(7, -2), B=(-6, 0), and C=(-3, -10). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.407", "style": "rule" }
{ "index": 1123, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-9, 7), B=(-2, -10), and C=(5, 0), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "57.37°", "style": "rule" }
{ "index": 1124, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-3, 3), B=(-8, -4), and C=(-8, 8), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "35.54°", "style": "rule" }
{ "index": 1125, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(9, -7), B=(7, 9), and C=(8, -3), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.36°", "style": "rule" }
{ "index": 1126, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, -7), B=(1, -4), and C=(7, 1). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.981", "style": "rule" }
{ "index": 1127, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-5, -6), B=(-3, 3), and C=(-8, 2). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.881", "style": "rule" }
{ "index": 1128, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(2, 3), B=(-6, 8), and C=(-10, -4), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "76.43°", "style": "rule" }
{ "index": 1129, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(9, 5), B=(7, -2), and C=(-4, -9), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "138.42°", "style": "rule" }
{ "index": 1130, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-5, 2), B=(-4, 1), and C=(6, -10), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(248.000, 232.000)", "style": "rule" }
{ "index": 1131, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(3, -1), B=(6, -1), and C=(-2, -7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.865", "style": "rule" }
{ "index": 1132, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(8, 1), B=(-1, 4), and C=(-10, -3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-3.667, 16.000)", "style": "rule" }
{ "index": 1133, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-3, -6), B=(10, -8), and C=(-8, -6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.41°", "style": "rule" }
{ "index": 1134, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-2, 7), B=(5, -10), and C=(-3, 3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-19.622, -3.844)", "style": "rule" }
{ "index": 1135, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(5, 0), B=(-2, -2), and C=(4, -6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "49.64°", "style": "rule" }
{ "index": 1136, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-9, -7), B=(8, 10), and C=(-3, 9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "39.81°", "style": "rule" }
{ "index": 1137, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(2, 2), B=(-2, 1), and C=(4, 6), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(6.286, -3.143)", "style": "rule" }
{ "index": 1138, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-8, 1), B=(-3, 0), and C=(9, -9), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(17.909, 35.545)", "style": "rule" }
{ "index": 1139, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-3, -9), B=(-7, -2), and C=(9, 6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "86.82°", "style": "rule" }
{ "index": 1140, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-9, 4), B=(1, 10), and C=(9, -8), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-0.474, 7.789)", "style": "rule" }
{ "index": 1141, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-5, -2), B=(-9, -9), and C=(-2, 4), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.44°", "style": "rule" }
{ "index": 1142, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-9, -7), B=(5, 8), and C=(10, -1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(6.940, 1.856)", "style": "rule" }
{ "index": 1143, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-2, 10), B=(-8, -7), and C=(6, 3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(1.989, 4.416)", "style": "rule" }
{ "index": 1144, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(0, -4), B=(9, -2), and C=(-2, -9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "19.94°", "style": "rule" }
{ "index": 1145, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(6, -8), B=(5, 2), and C=(4, -8), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "11.42°", "style": "rule" }
{ "index": 1146, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(10, 6), B=(0, 2), and C=(8, 6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "4.76°", "style": "rule" }
{ "index": 1147, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, 6), B=(7, -9), and C=(-9, 0), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.078, 0.805)", "style": "rule" }
{ "index": 1148, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, 0), B=(8, -8), and C=(-7, -10), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-0.623, -2.826)", "style": "rule" }
{ "index": 1149, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-1, 0), B=(0, -3), and C=(-6, 5), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "18.43°", "style": "rule" }
{ "index": 1150, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(9, 1), B=(-3, 3), and C=(5, -3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(4.714, -4.714)", "style": "rule" }
{ "index": 1151, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(0, 7), B=(-7, -9), and C=(-3, -10), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "80.41°", "style": "rule" }
{ "index": 1152, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(5, -1), B=(-6, 6), and C=(-8, -6), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-3.877, 0.479)", "style": "rule" }
{ "index": 1153, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-2, 5), B=(9, 6), and C=(1, -3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.877", "style": "rule" }
{ "index": 1154, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-3, 7), B=(3, -8), and C=(-4, 3), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "10.67°", "style": "rule" }
{ "index": 1155, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(9, 2), B=(-5, 7), and C=(8, 3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(17.444, 29.444)", "style": "rule" }
{ "index": 1156, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-8, 6), B=(-3, 3), and C=(-8, 2), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "42.27°", "style": "rule" }
{ "index": 1157, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 0), B=(-7, 10), and C=(-8, -4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-4.880, 0.991)", "style": "rule" }
{ "index": 1158, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-5, 1), B=(-6, 2), and C=(4, -9). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.034", "style": "rule" }
{ "index": 1159, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(5, 3), B=(-4, -9), and C=(3, -1), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(49.000, -35.500)", "style": "rule" }
{ "index": 1160, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(1, -5), B=(-2, 1), and C=(5, 7). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.100", "style": "rule" }
{ "index": 1161, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(10, 2), B=(7, -1), and C=(-3, 3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(6.571, -6.571)", "style": "rule" }
{ "index": 1162, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(3, 2), B=(10, 4), and C=(1, -9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "39.36°", "style": "rule" }
{ "index": 1163, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(5, -1), B=(-1, -9), and C=(6, -10), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.935, -8.452)", "style": "rule" }
{ "index": 1164, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(10, -10), B=(-9, -1), and C=(-3, -8), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "24.05°", "style": "rule" }
{ "index": 1165, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-8, 10), B=(2, 5), and C=(2, -2). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.071", "style": "rule" }
{ "index": 1166, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-10, -1), B=(0, 4), and C=(0, -6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "63.43°", "style": "rule" }
{ "index": 1167, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(6, 5), B=(8, -9), and C=(-10, 3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "4.393", "style": "rule" }
{ "index": 1168, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(10, 5), B=(4, 8), and C=(-2, 0), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.091, 10.182)", "style": "rule" }
{ "index": 1169, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, 8), B=(2, -6), and C=(6, 7), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(3.789, 6.526)", "style": "rule" }
{ "index": 1170, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(5, 7), B=(-6, 0), and C=(9, 8), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "4.40°", "style": "rule" }
{ "index": 1171, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(10, -7), B=(-8, 2), and C=(10, 3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(9.500, 2.000)", "style": "rule" }
{ "index": 1172, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, 2), B=(-7, 0), and C=(-9, 7), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-7.632, -1.895)", "style": "rule" }
{ "index": 1173, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-7, -9), B=(-4, -8), and C=(3, 7), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "133.45°", "style": "rule" }
{ "index": 1174, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(6, -5), B=(-4, 4), and C=(6, 5). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.985", "style": "rule" }
{ "index": 1175, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-6, -7), B=(6, -10), and C=(1, -8), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "7.77°", "style": "rule" }
{ "index": 1176, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(2, -4), B=(1, 7), and C=(-8, -3), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "47.18°", "style": "rule" }
{ "index": 1177, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(10, -1), B=(-7, -1), and C=(-3, -2), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-3.000, -53.000)", "style": "rule" }
{ "index": 1178, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(3, -2), B=(9, 9), and C=(-7, 8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "3.981", "style": "rule" }
{ "index": 1179, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(5, 3), B=(10, 8), and C=(-10, 0), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "23.20°", "style": "rule" }
{ "index": 1180, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(10, 4), B=(6, 8), and C=(5, -4), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "49.76°", "style": "rule" }
{ "index": 1181, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-6, 2), B=(-9, 3), and C=(3, 8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.001", "style": "rule" }
{ "index": 1182, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(10, 0), B=(7, 5), and C=(0, -9), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(12.727, -1.364)", "style": "rule" }
{ "index": 1183, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-4, -1), B=(-1, 3), and C=(6, 4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-6.000, 13.000)", "style": "rule" }
{ "index": 1184, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-10, -3), B=(-6, 0), and C=(7, 0), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "143.13°", "style": "rule" }
{ "index": 1185, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(0, -5), B=(1, 3), and C=(1, 4). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.055", "style": "rule" }
{ "index": 1186, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(3, 7), B=(-7, -2), and C=(0, -5). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.781", "style": "rule" }
{ "index": 1187, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(4, -7), B=(9, -2), and C=(3, 9), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "106.39°", "style": "rule" }
{ "index": 1188, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(8, -2), B=(-9, 3), and C=(10, 2), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(7.821, -5.410)", "style": "rule" }
{ "index": 1189, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-6, -1), B=(2, -6), and C=(-9, -1), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "7.56°", "style": "rule" }
{ "index": 1190, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, 6), B=(-1, -5), and C=(10, -1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(1.545, -1.000)", "style": "rule" }
{ "index": 1191, "split": "train" }
advanced_geometry/orthocenter
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-7, -10), B=(-8, 8), and C=(-9, -8), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "(-24.882, -8.882)", "style": "rule" }
{ "index": 1192, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(3, 7), B=(8, 5), and C=(2, -6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "83.19°", "style": "rule" }
{ "index": 1193, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(5, 5), B=(-2, 6), and C=(0, 7), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "34.70°", "style": "rule" }
{ "index": 1194, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(2, -1), B=(-3, -3), and C=(1, 6). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "1.659", "style": "rule" }
{ "index": 1195, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(5, -4), B=(1, 1), and C=(-7, 9). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "0.226", "style": "rule" }
{ "index": 1196, "split": "train" }
advanced_geometry/incircle_radius
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-2, 4), B=(-10, -9), and C=(-7, 5). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "2.105", "style": "rule" }
{ "index": 1197, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(4, 1), B=(8, 6), and C=(6, -9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "31.07°", "style": "rule" }
{ "index": 1198, "split": "train" }
advanced_geometry/angle_measure
[ { "content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(9, 5), B=(-4, -1), and C=(-2, -4), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>", "role": "user" } ]
deductive, inductive
{ "ground_truth": "81.09°", "style": "rule" }
{ "index": 1199, "split": "train" }