messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "In triangle ABC with coordinates A=(9, 1), B=(-3, -7), and C=(3, 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, coordi... | 19.44° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -2), B=(-6, 1), and C=(-8, -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,... | (-6.324, 2.378) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, -5), B=(-5, 2), and C=(10, -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... | 1.653 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, 8), B=(-5, -10), 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,... | 68.40° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 1), B=(-8, 5), and C=(-10, 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, coor... | 164.74° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, 10), B=(8, -4), and C=(-2, -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... | (-3.607, -3.033) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 10), B=(8, -5), and C=(7, 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 ... | 1.781 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, -3), B=(-8, 10), and C=(-2, 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... | 2.40° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 1), B=(-3, 0), and C=(9, -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... | 0.829 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, -7), B=(-7, -6), 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... | (-7.000, -211.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, 9), B=(7, 8), and C=(-10, -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, ... | 73.20° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -10), B=(-6, -4), 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 radi... | 1.941 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 7), B=(2, 10), and C=(1, 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, or ... | 69.15° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, -8), B=(9, -1), 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... | 4.97° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, 6), B=(9, -8), 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... | 0.748 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, -2), B=(9, -4), and C=(8, -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,... | (7.556, -9.778) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 8), B=(-3, 4), 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, or... | 26.57° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -10), B=(7, -10), and C=(-5, 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... | 39.81° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(9, -10), B=(-4, 5), and C=(5, 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... | (11.148, 9.328) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 6), B=(-4, -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... | (-0.134, -11.836) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 0), B=(7, -7), 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, or... | 46.22° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -6), B=(4, 7), and C=(-6, -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, ... | (6.257, -4.286) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -6), B=(8, 2), and C=(-8, -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, coordi... | 3.247 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, -4), B=(1, 0), and C=(-10, 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, coordin... | 0.860 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 8), B=(-8, 4), and C=(-2, -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... | 77.09° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, -4), B=(4, 9), and C=(1, 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, c... | (16.281, -13.105) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -5), B=(2, 6), and C=(-6, -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, coord... | 64.07° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, -4), B=(6, -1), and C=(-9, 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... | (12.000, 16.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, 1), B=(-10, 7), and C=(0, 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... | (9.000, 26.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 0), B=(-1, 8), and C=(-4, 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... | 1.04° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, -4), B=(-9, 5), and C=(9, 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... | 45.78° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, 6), B=(-3, -5), 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, coordin... | 1.897 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 4), B=(7, 3), and C=(-9, 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... | (-9.252, 5.709) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, -9), B=(1, 3), and C=(-9, 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 ... | 2.299 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, 5), B=(0, -3), and C=(1, -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, ... | (17.571, 11.643) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, 2), B=(10, 10), and C=(6, -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, ... | 14.04° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, -1), B=(-10, 6), and C=(-3, -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,... | 14.74° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 8), B=(-2, -5), and C=(-3, -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,... | (9.000, -15.154) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -9), B=(1, -1), and C=(7, 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... | (-59.000, 69.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, -8), B=(-5, 8), 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, ... | 61.33° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, -10), B=(8, 10), and C=(7, 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,... | (-433.000, 206.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, 4), B=(-6, -4), and C=(9, 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,... | (-22.125, 25.562) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, -10), B=(-3, 4), 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,... | 93.37° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -6), B=(-6, 9), and C=(-10, -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, coor... | 4.817 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, 6), B=(-4, -9), and C=(2, 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, ... | (49.500, -9.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, -8), B=(3, 10), and C=(6, 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, coord... | 44.52° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 7), B=(9, -6), and C=(-8, -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, ... | 35.73° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 10), B=(2, 5), and C=(2, -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, ... | (8.000, 10.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, -5), B=(4, -4), and C=(4, -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... | 0.806 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -9), B=(-9, -6), 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, coo... | 12.09° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, 2), B=(-8, -2), and C=(8, -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 radiu... | 2.294 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, -5), B=(-10, 7), 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... | (0.429, -3.429) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 7), B=(-5, 7), and C=(-8, -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, ... | 102.09° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, -10), B=(-3, -6), 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 ang... | (-1.667, -10.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 8), B=(-6, 8), and C=(6, 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, coordina... | 1.438 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-1, -9), B=(-5, -8), and C=(-5, 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, co... | (-9.750, -9.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-5, 4), B=(-6, -2), and C=(5, -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,... | (-4.692, 0.615) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 4), B=(3, 9), and C=(7, 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... | (-8.000, -13.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, -2), B=(0, 4), and C=(2, 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, or ... | 8.13° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 10), B=(2, 2), and C=(-8, 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... | (2.176, -1.176) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 0), B=(2, -6), and C=(3, 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, or... | 36.03° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -8), B=(0, 6), and C=(-6, -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,... | (4.111, -10.444) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 7), B=(3, -4), and C=(2, 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... | 34.14° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 5), B=(8, -9), 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, coord... | (6.211, 5.316) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, 3), B=(1, -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, o... | 56.31° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 3), B=(-9, -1), 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 radiu... | 0.397 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 3), B=(0, 9), and C=(2, 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, coordinat... | 0.912 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, -5), B=(1, -6), and C=(-4, 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,... | 45.00° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, 4), B=(-5, -2), 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, o... | 57.26° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, 4), B=(-1, -9), and C=(-2, -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... | (15.333, -11.333) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 7), B=(-7, -2), and C=(0, -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... | (-1.452, -3.387) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 9), B=(-6, 3), and C=(0, -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 radiu... | 1.224 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, -10), B=(0, -4), and C=(2, -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, ... | 106.50° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 1), B=(5, -10), and C=(-3, 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... | 2.651 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 10), B=(-8, 8), 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, coord... | 64.98° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, -8), B=(-2, 10), and C=(5, 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... | 3.776 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, -5), B=(-8, 0), and C=(2, 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... | (-3.692, -2.692) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 2), B=(-6, -5), and C=(6, -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... | 2.329 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, -2), B=(-6, 1), and C=(5, -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, o... | 11.92° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -4), B=(10, 8), 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, ... | 26.73° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, -2), B=(10, -2), 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, ... | 40.24° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(2, 0), B=(-6, -5), and C=(-7, 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... | (-6.000, -1.600) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 1), B=(-1, 3), 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... | 0.619 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 5), B=(9, -8), and C=(-9, -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, ... | (9.778, -9.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, 7), B=(6, 8), and C=(-3, 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... | (-3.857, 21.143) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 10), B=(-2, 7), and C=(8, 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... | (8.556, 2.778) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 0), B=(-6, 2), 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, coordin... | 53.97° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, -3), B=(-10, 3), and C=(6, 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, ... | 56.31° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, -6), B=(-7, 4), and C=(-1, 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... | 50.60° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -2), B=(6, 1), and C=(-9, 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, coordi... | (3.818, -2.545) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, -10), B=(1, -1), and C=(-8, -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, coord... | 2.636 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 6), B=(5, 1), and C=(3, -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, coordina... | 3.388 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, 9), B=(7, 1), and C=(-6, 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, coordi... | (-5.000, 2.500) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -7), B=(4, 2), and C=(-9, 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 ... | 3.378 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 2), B=(-10, 9), and C=(-6, 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... | 23.04° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 10), B=(4, -6), 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... | 1.917 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -7), B=(8, -4), and C=(5, -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... | 9.46° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(7, -2), B=(10, 5), 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,... | (12.958, -11.268) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 7), B=(4, 8), and C=(7, -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... | 1.684 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-4, -2), B=(-6, -9), 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... | 1.544 | Puzzle | advanced_geometry |
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