messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Given a triangle with vertices A=(-9, 1), B=(4, 1), and C=(-1, 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... | 30.96° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, -7), B=(7, 5), 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, coordina... | 0.805 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -4), B=(5, 7), 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... | 0.235 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-7, 9), B=(-7, -3), and C=(8, -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... | (-15.867, -10.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 2), B=(8, 4), and C=(-8, 1), 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, coordin... | 11.18° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, -8), B=(-6, 7), and C=(-9, -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 angl... | (-714.000, 184.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, -10), B=(-2, -3), and C=(-3, -6), 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, c... | 17.10° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, 4), B=(-8, 0), and C=(5, 6). 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 ... | 0.348 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(9, -5), B=(2, -10), and C=(5, 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, coord... | (8.455, -4.836) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 8), B=(-8, 3), and C=(-1, 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... | 11.31° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 10), B=(0, 7), 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, coordi... | (1.326, 6.905) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 1), B=(-7, 8), and C=(8, -10), 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, coord... | (20.372, 12.977) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, 7), B=(-6, 7), and C=(2, -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, ... | (2.000, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, 7), B=(-7, 6), and C=(-10, 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, coordi... | 0.196 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, -1), B=(9, -6), and C=(-3, -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... | (9.000, 35.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, -1), B=(-2, 0), and C=(10, -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, coo... | (10.750, 0.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, 2), B=(-5, -6), and C=(5, -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, coord... | 55.36° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, -3), B=(-4, -9), 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, co... | (-5.000, -8.333) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-4, -7), B=(10, 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, coordi... | 0.116 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, 8), B=(4, -2), and C=(4, -8). 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, coordina... | 0.550 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 8), B=(1, -2), and C=(-10, -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,... | 58.24° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, 1), B=(4, 6), and C=(-9, 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, c... | (-2.621, -3.931) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, 10), B=(9, 2), 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, coordi... | 3.819 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, 1), B=(-2, 1), and C=(-4, -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, coordi... | 2.937 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -2), B=(-10, -3), and C=(-8, -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, coordinate... | 18.43° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, -2), B=(4, 5), and C=(-4, 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, coordi... | (7.667, 7.333) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 0), B=(8, 0), and C=(0, 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 ... | 7.13° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 4), B=(-3, 6), and C=(-4, 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, coordin... | 0.721 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, -2), B=(3, -9), and C=(2, -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, ... | (-33.000, -9.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, -4), B=(-5, 9), and C=(-6, 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, coordin... | 0.445 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, -6), B=(-1, -3), and C=(1, 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, coord... | 125.54° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -8), B=(6, 7), and C=(9, 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 ... | 63.97° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, -9), B=(-1, 0), and C=(2, 1). 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 ... | 1.327 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(2, -5), B=(2, -4), and C=(-10, -3), 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, coo... | (2.167, -3.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, 7), B=(-5, 2), and C=(6, 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, coordinat... | 1.259 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, -9), B=(-9, 3), and C=(7, -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,... | 28.29° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, -7), B=(-3, 6), 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, coordina... | 2.672 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 4), B=(8, -10), and C=(5, -5), 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, o... | 22.83° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, -2), B=(-10, 5), and C=(7, 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, coor... | (18.308, 33.308) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, -3), B=(3, -4), 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, coor... | 42.40° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, -4), B=(-8, 9), and C=(-7, 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, ... | 92.29° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-2, 5), B=(10, -9), and C=(9, 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, ... | 37.59° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -8), B=(9, 6), and C=(6, -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, coordi... | 4.64° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-2, -1), B=(6, -3), and C=(-3, -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, coo... | (-2.077, -0.308) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, 6), B=(6, 3), and C=(-9, -3), 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, coord... | (-5.919, 8.297) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, -9), B=(5, -10), and C=(6, 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, coor... | 86.25° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 9), B=(6, -7), and C=(8, -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... | 109.44° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 7), B=(-2, -7), and C=(-3, -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, coordi... | 0.460 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -4), B=(6, -7), and C=(7, 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... | 29.60° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 7), B=(6, 0), and C=(8, 0), 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, co... | (-4.000, -17.143) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, 1), B=(6, 3), 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... | 65.22° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-9, -8), B=(1, -1), and C=(-6, 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, coor... | (0.194, -0.849) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 1), B=(8, 6), 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 ... | 31.07° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, -1), B=(5, 3), and C=(6, -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, coordin... | 2.101 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, 2), B=(7, 4), 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, coo... | (4.667, 4.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 7), B=(-6, 1), and C=(4, 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 ... | 2.215 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, -6), B=(-5, 3), and C=(-9, -7), 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,... | (-4.500, -3.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 2), B=(5, 3), and C=(-4, -8). 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, coordina... | 1.526 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, 4), B=(-1, 2), and C=(-1, -4). 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 radiu... | 1.441 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, -8), B=(8, 3), and C=(2, 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, coordi... | (-1.816, 10.551) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -9), B=(-1, 9), and C=(-2, -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... | (-2.439, -8.268) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, 10), B=(3, 0), and C=(-8, -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 radiu... | 1.220 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 0), B=(9, 2), and C=(-2, -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... | 17.59° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, 7), B=(-1, -3), and C=(-5, 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, ... | (1.000, 6.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, 0), B=(8, 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, coordina... | 0.223 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, 2), B=(-10, -5), and C=(4, 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, ... | 33.69° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, 4), B=(-3, -2), 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, coo... | 135.00° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, 4), B=(-2, 8), and C=(6, -3), 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, coordi... | (16.941, 13.412) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -9), B=(8, 6), and C=(-4, -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, coordi... | 2.295 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -7), B=(0, -7), and C=(-1, -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, coor... | 116.57° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, -1), B=(-9, 7), and C=(8, -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, coord... | (26.483, 30.655) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 4), B=(0, -7), and C=(-10, 7), 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... | (-25.400, -7.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, -1), B=(-4, 0), and C=(0, -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... | (-2.773, 1.091) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, -4), B=(2, 6), and C=(-7, -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, coord... | 50.71° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 7), B=(1, 1), and C=(0, -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, c... | (-30.316, 10.211) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, -5), B=(-4, -2), and C=(-8, 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, co... | (-7.750, -0.500) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, -5), B=(10, -6), 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, coord... | 0.429 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 7), B=(2, -8), and C=(10, 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, coordin... | 5.280 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -2), B=(8, 9), and C=(7, -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, o... | 49.35° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 0), B=(2, -7), and C=(8, 3), 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, coordin... | (39.500, -19.500) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -5), B=(7, 3), and C=(-10, 10), 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, coor... | (7.478, 3.446) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-5, 5), B=(-5, -3), 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... | (-21.250, 10.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, 10), B=(5, -3), 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, coo... | 23.04° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -7), B=(-7, 4), and C=(-5, 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, ... | 158.20° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -8), B=(-7, -4), and C=(8, 0), 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,... | (-1.100, -11.375) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, -7), B=(-6, -6), 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, coor... | (3.889, -25.778) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -5), B=(1, 7), and C=(9, 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, co... | (18.000, 7.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 2), B=(-5, 7), and C=(8, 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, coordinat... | 0.301 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, -6), B=(9, -7), and C=(0, 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, coord... | 84.29° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, -2), B=(-9, 2), and C=(-3, -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... | 24.78° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -10), B=(-7, 10), and C=(5, -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, coo... | 9.69° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, -6), B=(-4, -6), and C=(-3, -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 radi... | 0.475 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 6), B=(6, 2), and C=(7, 9). 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... | 1.140 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-1, 5), B=(1, 0), and C=(-4, -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, coord... | (5.286, -1.286) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, -7), B=(-3, -3), and C=(6, 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, ... | (2.875, -4.469) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, -1), B=(10, 1), 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,... | (-80.000, 71.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -10), B=(-5, 1), and C=(-3, -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,... | 26.33° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, -7), B=(-7, -9), and C=(9, -1), 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, coor... | 12.53° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, -10), B=(0, -3), and C=(5, -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,... | 141.55° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, -2), B=(3, 10), and C=(2, 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, coordi... | 0.461 | Puzzle | advanced_geometry |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.