Datasets:
jamescai20
/
tts-reasoning

Dataset card Data Studio Files Community
1
Search is not available for this dataset
data_source
stringclasses
10 values
prompt
listlengths
1
1
ability
stringclasses
2 values
reward_model
dict
extra_info
dict
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=(8, -7), and C=(9, 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": "(7.169, -6.481)", "style": "rule" }
{ "index": 700, "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, -10), and C=(2, 3), 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": "16.27°", "style": "rule" }
{ "index": 701, "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=(7, 0), B=(6, -7), and C=(-10, 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": "(6.333, -1.333)", "style": "rule" }
{ "index": 702, "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=(7, 1), B=(-5, -10), and C=(3, 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": "2.744", "style": "rule" }
{ "index": 703, "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=(6, -5), B=(2, 4), and C=(8, 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": "(3.065, 3.806)", "style": "rule" }
{ "index": 704, "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=(4, -2), and C=(-1, 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": "(-35.565, -35.478)", "style": "rule" }
{ "index": 705, "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, 0), B=(-1, 2), and C=(-9, 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": "0.479", "style": "rule" }
{ "index": 706, "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=(4, 10), B=(-5, 3), and C=(0, 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": "(-5.000, 16.429)", "style": "rule" }
{ "index": 707, "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, -6), B=(-3, 4), and C=(8, -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": "(-7.000, -16.000)", "style": "rule" }
{ "index": 708, "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=(0, 3), and C=(7, 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": "35.84°", "style": "rule" }
{ "index": 709, "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, 0), B=(2, -8), and C=(10, -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": "107.10°", "style": "rule" }
{ "index": 710, "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, 0), B=(-5, -9), and C=(7, -9), 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": "(-8.000, -14.000)", "style": "rule" }
{ "index": 711, "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, -6), B=(10, -5), and C=(-7, -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": "0.204", "style": "rule" }
{ "index": 712, "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, 0), B=(-1, -8), 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": "20.56°", "style": "rule" }
{ "index": 713, "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, 9), B=(9, 1), and C=(-7, -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": "(0.704, 3.593)", "style": "rule" }
{ "index": 714, "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=(7, -5), B=(4, -4), and C=(4, -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": "(2.667, -5.000)", "style": "rule" }
{ "index": 715, "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, 6), B=(-2, 6), and C=(5, 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": "(5.000, -85.000)", "style": "rule" }
{ "index": 716, "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=(7, -8), B=(0, -4), and C=(4, -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": "0.308", "style": "rule" }
{ "index": 717, "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=(-7, 0), B=(-7, -4), and C=(-10, 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": "0.838", "style": "rule" }
{ "index": 718, "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, -3), B=(9, -2), and C=(8, 0). 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": "0.156", "style": "rule" }
{ "index": 719, "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=(1, -5), B=(2, -3), and C=(-8, 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": "80.13°", "style": "rule" }
{ "index": 720, "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, 5), B=(-7, -9), and C=(6, -7), 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": "93.35°", "style": "rule" }
{ "index": 721, "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, -8), B=(3, 10), and C=(6, 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": "44.52°", "style": "rule" }
{ "index": 722, "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, -3), B=(3, -2), and C=(-5, -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": "0.667", "style": "rule" }
{ "index": 723, "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, 1), B=(-2, 0), and C=(-6, -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": "(-3.200, 1.800)", "style": "rule" }
{ "index": 724, "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=(-7, -7), B=(10, 5), and C=(-4, 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": "31.13°", "style": "rule" }
{ "index": 725, "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, 4), B=(-1, -3), and C=(5, -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": "1.501", "style": "rule" }
{ "index": 726, "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, 9), B=(10, -7), and C=(7, 1). 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": "1.604", "style": "rule" }
{ "index": 727, "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, 4), B=(-6, -9), 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": "(-5.000, -8.615)", "style": "rule" }
{ "index": 728, "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, -5), B=(4, 2), and C=(-8, -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": "(-6.444, -3.222)", "style": "rule" }
{ "index": 729, "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=(7, 0), B=(-9, -4), and C=(-6, 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": "1.508", "style": "rule" }
{ "index": 730, "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, 1), B=(0, 7), and C=(5, 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": "0.901", "style": "rule" }
{ "index": 731, "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, -7), B=(8, 5), and C=(4, -5), 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": "(10.909, -15.364)", "style": "rule" }
{ "index": 732, "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=(10, 3), and C=(3, -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": "(4.020, -12.549)", "style": "rule" }
{ "index": 733, "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, 3), B=(-7, 5), and C=(-10, 8), 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": "(-13.429, -19.429)", "style": "rule" }
{ "index": 734, "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, 4), B=(1, 8), and C=(-2, 0). 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": "1.735", "style": "rule" }
{ "index": 735, "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, -6), B=(1, -4), and C=(3, 10). 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": "0.124", "style": "rule" }
{ "index": 736, "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=(7, -5), B=(2, 6), and C=(-4, -3), 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": "58.13°", "style": "rule" }
{ "index": 737, "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=(4, -4), and C=(3, 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": "1.469", "style": "rule" }
{ "index": 738, "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=(-6, 0), and C=(5, -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": "1.533", "style": "rule" }
{ "index": 739, "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=(-7, -2), B=(0, 6), and C=(1, 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": "67.75°", "style": "rule" }
{ "index": 740, "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, -4), B=(-4, 4), and C=(2, -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": "13.39°", "style": "rule" }
{ "index": 741, "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, -9), B=(-1, -3), and C=(-1, 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": "(-12.400, -9.000)", "style": "rule" }
{ "index": 742, "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=(-7, -5), B=(2, -10), and C=(-6, 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": "36.98°", "style": "rule" }
{ "index": 743, "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=(10, -4), and C=(-5, 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": "(-5.606, 2.242)", "style": "rule" }
{ "index": 744, "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, 10), B=(5, -6), and C=(1, 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": "(1.250, 9.000)", "style": "rule" }
{ "index": 745, "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, -10), B=(1, -5), and C=(10, -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": "45.00°", "style": "rule" }
{ "index": 746, "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, -9), B=(5, -6), and C=(2, 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": "(-10.429, -13.714)", "style": "rule" }
{ "index": 747, "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=(-1, 4), B=(-8, 5), and C=(7, 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": "19.44°", "style": "rule" }
{ "index": 748, "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, 9), B=(-10, -4), and C=(-5, -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": "76.53°", "style": "rule" }
{ "index": 749, "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, 3), B=(6, -7), and C=(3, 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": "12.99°", "style": "rule" }
{ "index": 750, "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, -7), B=(7, -10), and C=(4, -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": "51.01°", "style": "rule" }
{ "index": 751, "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, 6), B=(-8, -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": "(-5.185, 6.508)", "style": "rule" }
{ "index": 752, "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, 5), B=(-5, -1), 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": "(-1.824, -2.765)", "style": "rule" }
{ "index": 753, "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, 5), B=(7, 9), and C=(2, 3), 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": "2.94°", "style": "rule" }
{ "index": 754, "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, -6), B=(-8, 5), and C=(8, 5), 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": "47.73°", "style": "rule" }
{ "index": 755, "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, 3), B=(-9, 3), 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, 1.800)", "style": "rule" }
{ "index": 756, "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=(10, 2), B=(5, -10), and C=(-5, 2). 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": "4.127", "style": "rule" }
{ "index": 757, "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, 8), B=(-9, 5), and C=(4, 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": "7.70°", "style": "rule" }
{ "index": 758, "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=(9, -8), B=(-6, 0), and C=(6, -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": "1.039", "style": "rule" }
{ "index": 759, "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=(-6, 7), B=(1, 0), and C=(-1, -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": "113.20°", "style": "rule" }
{ "index": 760, "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, 5), B=(6, 3), and C=(-7, -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": "2.726", "style": "rule" }
{ "index": 761, "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=(4, -8), B=(0, -10), 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": "(-2.045, -14.909)", "style": "rule" }
{ "index": 762, "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=(-3, -8), B=(-2, -9), and C=(4, 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": "(-6.421, -6.421)", "style": "rule" }
{ "index": 763, "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, 8), B=(-1, 7), and C=(0, 9), 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": "(-0.632, 3.316)", "style": "rule" }
{ "index": 764, "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, -5), B=(-3, -1), and C=(-5, 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": "(4.200, -2.200)", "style": "rule" }
{ "index": 765, "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, 10), B=(-1, -6), and C=(4, -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": "(13.600, -6.000)", "style": "rule" }
{ "index": 766, "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, -1), and C=(10, 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": "1.230", "style": "rule" }
{ "index": 767, "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=(8, 4), B=(-9, -5), and C=(10, -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": "18.92°", "style": "rule" }
{ "index": 768, "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, 6), B=(6, 3), and C=(-9, -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": "2.967", "style": "rule" }
{ "index": 769, "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, 9), B=(-1, 1), and C=(10, -1). 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": "2.890", "style": "rule" }
{ "index": 770, "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=(-10, 9), B=(9, 2), and C=(2, -2). 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": "2.803", "style": "rule" }
{ "index": 771, "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, -6), B=(-3, 10), and C=(-10, 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": "24.37°", "style": "rule" }
{ "index": 772, "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=(-1, -9), B=(9, -1), 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": "3.505", "style": "rule" }
{ "index": 773, "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=(9, -7), B=(3, 5), and C=(-8, -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": "4.469", "style": "rule" }
{ "index": 774, "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=(9, 0), B=(1, -4), and C=(-2, 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": "3.093", "style": "rule" }
{ "index": 775, "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=(7, 0), B=(7, 5), and C=(-8, 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": "(7.933, 7.000)", "style": "rule" }
{ "index": 776, "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, -6), B=(-1, 1), and C=(-6, -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": "(-7.296, -0.259)", "style": "rule" }
{ "index": 777, "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=(0, 6), B=(5, -7), and C=(-4, -3). 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": "2.885", "style": "rule" }
{ "index": 778, "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, 5), B=(-1, 1), 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": "124.02°", "style": "rule" }
{ "index": 779, "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, 0), B=(-5, 4), 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": "0.548", "style": "rule" }
{ "index": 780, "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, -3), B=(-5, -8), and C=(7, 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": "(7.909, -1.545)", "style": "rule" }
{ "index": 781, "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=(1, -9), and C=(-6, -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": "66.37°", "style": "rule" }
{ "index": 782, "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, -1), B=(8, -7), and C=(10, -4), 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": "(19.000, -7.000)", "style": "rule" }
{ "index": 783, "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, -2), B=(5, 1), and C=(-6, -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": "124.59°", "style": "rule" }
{ "index": 784, "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, 5), B=(9, -9), and C=(6, 5), 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": "(9.000, 7.357)", "style": "rule" }
{ "index": 785, "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, -8), B=(-3, 8), and C=(-6, 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": "0.821", "style": "rule" }
{ "index": 786, "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=(-1, 5), B=(-4, 8), and C=(-10, -1). 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": "1.739", "style": "rule" }
{ "index": 787, "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, -2), B=(-2, 4), and C=(10, -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": "2.162", "style": "rule" }
{ "index": 788, "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=(1, 2), B=(10, -6), and C=(-10, -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": "3.505", "style": "rule" }
{ "index": 789, "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, 7), B=(0, 6), and C=(8, -3), 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": "54.08°", "style": "rule" }
{ "index": 790, "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, -1), B=(1, 8), and C=(-5, -7), 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": "63.43°", "style": "rule" }
{ "index": 791, "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, -3), B=(8, -5), and C=(7, -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": "(6.769, -8.385)", "style": "rule" }
{ "index": 792, "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=(1, -7), 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": "19.44°", "style": "rule" }
{ "index": 793, "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, 7), B=(10, -7), and C=(-10, -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": "(-9.300, -7.000)", "style": "rule" }
{ "index": 794, "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=(-7, 8), and C=(-2, 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": "38.66°", "style": "rule" }
{ "index": 795, "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, 0), B=(8, -1), 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": "66.37°", "style": "rule" }
{ "index": 796, "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=(10, -4), 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": "18.07°", "style": "rule" }
{ "index": 797, "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, 4), B=(7, 4), and C=(4, 1). 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": "1.052", "style": "rule" }
{ "index": 798, "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, 2), B=(-4, 8), and C=(-4, 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": "65.22°", "style": "rule" }
{ "index": 799, "split": "train" }