messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1 value | type stringclasses 1 value |
|---|---|---|---|
[
{
"content": "Given a triangle with vertices A=(-10, -1), B=(5, 4), and C=(-3, -9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 39.96° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, 5), B=(-3, -5), and C=(-10, -2), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 35.84° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 3), B=(6, -10), and C=(10, -7), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 98.13° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, 5), B=(3, -3), and C=(-9, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.239 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, 0), B=(4, -2), and C=(-2, 2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (4.250, -1.125) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 2), B=(-2, -9), and C=(-4, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-10.032, 1.710) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(1, 6), B=(-6, 2), and C=(8, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (0.444, 5.222) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, -3), B=(-6, -7), and C=(5, -5), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (3.833, -2.083) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, -8), B=(-3, -5), and C=(-5, 4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.860 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -9), B=(4, -6), and C=(-6, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (0.471, -6.941) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, 9), B=(-6, -4), and C=(10, -10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 5.228 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, -4), B=(1, -9), and C=(-3, -7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.442 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 5), B=(-7, 4), and C=(-8, 9), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 95.60° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, -2), B=(-10, -5), and C=(-3, 2), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 32.01° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, 4), B=(-1, -7), and C=(9, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-4.908, 3.943) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, 6), B=(10, -4), and C=(1, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (16.222, 10.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 10), B=(5, -6), and C=(1, 9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.795 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, 6), B=(-4, 4), and C=(-7, -5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-15.000, 11.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, -7), B=(-2, 4), and C=(5, 5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 122.57° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 8), B=(-4, -3), and C=(6, -8), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 96.58° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(0, 5), B=(-8, 8), and C=(-1, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-1.818, 1.818) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 5), B=(-4, 1), and C=(-9, 0). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.497 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -7), B=(-2, 7), and C=(8, 3), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 38.45° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 2), B=(-6, -3), and C=(-7, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-4.437, 0.797) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -4), B=(-9, -1), and C=(3, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (2.455, 4.727) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, -7), B=(-10, 1), and C=(-1, 7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 67.38° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -8), B=(7, 3), and C=(1, 7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.505 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 8), B=(4, -8), and C=(-10, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (5.389, 5.191) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, -5), B=(-2, -10), and C=(-7, 10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.986 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -5), B=(-6, 7), and C=(-7, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-3.625, -4.875) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 4), B=(-3, 6), and C=(4, 0). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.119 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(2, -5), B=(2, 1), and C=(7, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-20.400, 9.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, -10), B=(6, 1), and C=(10, 8), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 170.24° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -6), B=(-5, -10), and C=(-3, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 68.73° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -7), B=(2, -6), and C=(0, -6), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 11.31° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 10), B=(6, 0), and C=(9, -3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.088 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 6), B=(-3, 9), and C=(0, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 66.99° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, -4), B=(-3, 5), and C=(-5, 0), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 7.25° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 5), B=(-1, 7), and C=(-2, 10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.680 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -10), B=(-6, 9), and C=(9, -7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.681 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, -8), B=(1, 6), and C=(3, -6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-10.125, -10.688) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -2), B=(-3, -8), and C=(2, 7), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 46.79° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 4), B=(-4, -4), and C=(6, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.489 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 10), B=(-8, 4), and C=(3, -8), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 81.18° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 7), B=(-8, -4), and C=(10, 9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 21.69° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 0), B=(-5, 7), and C=(-9, -4), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 68.80° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -2), B=(-5, -4), and C=(2, 4), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.81° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -4), B=(-10, 9), and C=(7, -1). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.361 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -1), B=(-4, 4), and C=(3, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (3.048, -5.867) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, -5), B=(9, -2), and C=(9, 0), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (11.500, -5.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, -10), B=(3, -5), and C=(4, 2). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.089 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, 3), B=(-2, 1), and C=(4, -2), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (3.833, -1.333) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, 1), B=(3, -4), and C=(4, -7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.195 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-4, 7), B=(-9, -6), and C=(1, -3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.235 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 10), B=(-8, -1), and C=(2, 7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 18.87° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 8), B=(-9, 5), and C=(-3, -4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.910 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, 8), B=(-5, 2), and C=(4, -3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 119.05° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -6), B=(6, 9), and C=(-10, 9), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 82.41° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -10), B=(1, 2), and C=(-4, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.875 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-4, -4), B=(5, -9), and C=(4, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.686 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 3), B=(-10, 1), and C=(7, 5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.70° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, -2), B=(-9, 3), and C=(10, 2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.892 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, 2), B=(8, -2), and C=(4, -4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (2.667, -7.333) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 2), B=(-5, 10), and C=(-1, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (10.273, 23.091) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, -1), B=(-1, 6), and C=(5, 3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 18.43° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 10), B=(-1, 5), and C=(-10, -2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 127.87° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 7), B=(8, 7), and C=(4, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 14.04° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-7, -8), B=(8, 9), and C=(4, -2), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (23.278, -19.010) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -10), B=(3, 8), and C=(-2, -1), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-34.400, 8.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 3), B=(-2, 8), and C=(2, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.644 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, 3), B=(10, -10), and C=(0, -9), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 35.20° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, 10), B=(-5, 3), and C=(0, 10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.166 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 2), B=(7, 8), and C=(-10, 4), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 43.07° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 1), B=(1, 6), and C=(-7, 3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 91.25° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, 4), B=(-10, 8), and C=(0, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-23.034, -8.759) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, -7), B=(-1, 9), and C=(7, -2), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 39.60° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, 6), B=(-7, -6), and C=(-9, -5). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.996 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 4), B=(-2, -8), and C=(-8, 1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-2.600, -4.400) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, 8), B=(3, 1), and C=(3, -5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 156.80° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 5), B=(4, 8), and C=(-2, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.222 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, 4), B=(-1, -9), and C=(-6, -3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.993 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 3), B=(10, -6), and C=(0, -5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 36.28° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 10), B=(5, 9), and C=(1, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-3.273, 14.091) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-6, -6), B=(-4, 1), and C=(-6, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (4.500, 1.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 10), B=(7, -1), and C=(4, 8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (4.000, 8.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, 7), B=(-8, -5), and C=(4, -7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 104.23° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 5), B=(-1, 0), and C=(6, -9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 173.09° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -6), B=(-6, 8), and C=(-1, -8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 2.287 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 9), B=(-2, 1), and C=(9, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 3.010 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 3), B=(2, -2), and C=(-4, 3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 100.39° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-9, 0), B=(0, 7), and C=(-7, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-15.273, 14.636) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 5), B=(-9, 0), and C=(5, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.719 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -9), B=(2, 1), and C=(-1, -2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.795 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 2), B=(8, 3), and C=(-2, -3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.872 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -1), B=(1, -1), and C=(9, -7), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 143.13° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 8), B=(-3, -9), and C=(5, 8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (-3.000, 14.118) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 4), B=(1, 5), and C=(-7, 5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | (3.000, 25.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, -6), B=(9, 3), and C=(6, -8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.724 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, -3), B=(5, 4), and C=(-4, 1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 9.87° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 10), B=(8, -7), and C=(3, -4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.788 | Puzzle | advanced_geometry |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.