messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 8), B=(6, -4), and C=(-10, 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... | 4.314 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 6), B=(-3, 9), and C=(5, 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... | 0.980 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -4), B=(-4, 0), and C=(3, -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, coord... | 2.009 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 1), B=(10, -3), 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, coordin... | 0.626 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, 9), B=(-4, 8), and C=(5, 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, coordinat... | 2.171 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, 9), B=(-5, -6), 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, coo... | 30.38° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 7), B=(-5, 8), and C=(-6, -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, coord... | (-5.149, 8.215) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, -1), B=(2, -8), 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, coo... | (7.000, 7.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, -9), B=(-6, 8), 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,... | 41.24° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, 3), B=(-1, 10), and C=(-5, 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... | 0.76° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -10), B=(-5, -8), and C=(-9, -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 ra... | 1.094 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-6, 9), B=(-3, 5), and C=(-3, -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... | (19.667, 9.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, -1), B=(1, 2), and C=(5, -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... | 1.697 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -8), B=(1, -3), and C=(-4, 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... | (0.000, -3.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 9), B=(7, 5), and C=(-5, -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, c... | (9.364, 3.182) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 3), B=(8, 9), and C=(9, -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, coordin... | (-3.725, 2.604) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 3), B=(-6, 5), and C=(-2, 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... | 21.80° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, 1), B=(7, 10), and C=(-5, 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 ... | 2.522 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, -5), B=(-5, -7), and C=(-5, 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, coo... | 45.00° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(8, -7), B=(-10, -6), and C=(6, 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, coor... | 32.54° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -10), B=(-2, -5), and C=(-1, 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, co... | 135.00° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 3), B=(-3, -7), 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,... | (-13.000, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(7, 10), and C=(-6, -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 radi... | 3.158 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 7), B=(9, -6), and C=(8, 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 radius a... | 1.277 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -5), B=(8, -1), and C=(-8, 10), 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, co... | 47.04° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -8), B=(6, -4), and C=(8, -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 radiu... | 1.074 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, 2), B=(-6, -3), and C=(-5, -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, coo... | 57.53° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -9), B=(-8, -9), and C=(3, -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, ... | 19.98° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-2, -5), B=(4, -7), and C=(-8, 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... | (-16.091, -16.273) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, 4), B=(-7, 6), and C=(3, 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, coordin... | 16.02° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-6, -5), B=(1, 8), and C=(-1, -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, coordi... | 2.342 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-1, 9), B=(7, -9), 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, coor... | (-8.508, -7.892) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, -8), B=(-9, -8), and C=(10, 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, ... | 40.10° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 6), B=(-9, 0), 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, ... | (-11.353, -2.941) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 10), 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,... | 23.68° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, 5), B=(6, 3), and C=(-3, -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, coord... | (-1.677, 0.258) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 3), B=(0, 6), 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, coordi... | 4.40° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, -3), B=(-5, 9), and C=(3, -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, o... | 13.41° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 7), B=(7, -8), and C=(-3, -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... | 53.27° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, 9), B=(8, 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, coordin... | 37.23° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, 4), B=(0, -4), and C=(-3, 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, coordi... | 61.74° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 3), B=(6, -9), and C=(-9, 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,... | (-15.000, -2.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, -1), B=(-7, -10), and C=(0, 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,... | 2.82° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 3), B=(-3, -1), and C=(1, 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, coordina... | 1.233 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, -8), B=(7, 10), 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, coordi... | 63.43° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, 1), B=(-7, -8), and C=(1, -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, coordin... | 1.178 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, -2), B=(-3, 4), and C=(4, -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... | 47.34° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 7), B=(3, 8), and C=(10, -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 ... | 0.663 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -6), B=(-5, 7), and C=(-2, -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, coord... | 3.701 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, 6), B=(7, -4), 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, coord... | (-0.390, 0.927) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 4), B=(-6, 10), 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, coordi... | 4.075 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, -5), B=(10, 2), 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, coord... | 30.32° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 2), B=(5, -10), and C=(-5, 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, coor... | (5.000, -2.167) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, 6), B=(-9, -2), and C=(6, -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, coor... | 78.37° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, -3), B=(-4, -1), and C=(8, -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... | (-6.000, 33.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -10), B=(4, -9), and C=(-5, 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... | (-9.684, -26.105) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, -7), B=(10, 4), and C=(-7, 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, coordin... | 3.844 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 5), B=(-10, 3), and C=(-9, -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... | (-9.229, 0.943) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, 5), B=(4, -10), 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, coordinates, o... | 59.35° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 3), B=(-8, 0), 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,... | (-22.667, -8.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-9, 8), B=(2, -7), and C=(-4, 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, coord... | (11.849, 17.623) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 8), 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 radius... | 3.641 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, 2), B=(-10, -4), and C=(-6, 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... | (-10.000, 7.333) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, 2), B=(10, 4), and C=(-5, 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... | 2.701 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, 4), B=(9, 8), and C=(-10, 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... | (7.970, -8.478) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 0), B=(-2, -8), 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... | 50.87° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, 8), B=(10, 6), and C=(1, 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, coordin... | (1.889, 6.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 6), B=(1, -5), and C=(9, 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 a... | 0.398 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, -8), B=(-6, 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... | 72.92° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, -10), B=(-1, -9), and C=(-8, 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 radi... | 1.069 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 4), B=(0, 10), and C=(5, 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... | 40.60° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -10), B=(-4, 6), 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, coord... | 69.30° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, 9), B=(-10, -4), and C=(7, 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, coo... | (-11.302, 14.223) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, -1), B=(-8, 7), 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... | (-9.679, -6.434) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, -8), B=(-2, 6), and C=(2, 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... | (-5.091, 5.455) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, -3), B=(5, -4), and C=(1, 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... | 61.59° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 10), B=(8, 9), and C=(-9, 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, coordin... | 3.414 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, -4), B=(7, -7), and C=(8, -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, ... | 94.40° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, -1), B=(3, 4), and C=(6, 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, c... | (22.429, -32.429) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-4, -9), B=(-1, -3), and C=(-3, -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, coor... | 0.222 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 10), B=(0, 9), and C=(9, 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, coordi... | 151.59° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -8), B=(0, -5), 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, c... | (2.513, -4.462) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 7), B=(-1, 3), and C=(-6, 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 radius ... | 1.022 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, 5), B=(5, 7), and C=(-5, -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 ... | 0.630 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 5), B=(7, 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 r... | 90.00° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-2, 10), B=(-1, 9), 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, coor... | (30.667, 21.667) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, -6), B=(-9, -1), and C=(-6, 0), 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,... | 108.43° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, 9), B=(3, -3), and C=(1, -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... | 74.05° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, 2), B=(4, -8), and C=(-6, 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, coord... | 14.66° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 4), B=(7, 4), and C=(4, 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, coordina... | (4.000, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 0), B=(1, -4), 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, c... | (2.778, -1.556) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 2), B=(-1, -5), and C=(-8, 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,... | (-22.000, -5.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -3), B=(-2, 2), and C=(10, -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, coor... | (-30.000, -54.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -10), B=(-7, 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, o... | 65.66° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -7), B=(1, -4), 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, ... | 69.44° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 1), B=(4, -10), 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... | 19.57° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, 5), B=(-2, -10), and C=(7, 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, coordin... | 2.189 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, 0), B=(6, -8), 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,... | 7.52° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, -6), B=(-9, -7), and C=(5, -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 radi... | 0.369 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 6), B=(-4, 10), and C=(5, 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, coor... | (-7.571, 27.857) | Puzzle | advanced_geometry |
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