id
stringlengths 27
27
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringlengths 3
7
| dataset
stringclasses 1
value |
|---|---|---|---|---|---|
geometry_polygon_train_0000
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDE is a regular 5-gon with center G and circumradius 6. Let P be the reflection of point B across point G. Let F be the perpendicular bisector of segment DA. Line Y passes through point B parallel to line F. Point Q is the reflection of point D across line Y. Line X is the reflection of line F across line Y. Let K be the reflection of line X across line F. Point O is the reflection of point P across line K. What is the length of segment QO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23.53
|
math
|
geometry_polygon_train_0001
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ACDEFGHIJK is a regular 10-gon with center B and circumradius 3. Line Y passes through points E and H. Let N be the midpoint of segment GD. Line R is the reflection of line Y across point N. Point L is the intersection of line R and segment IH. Find the distance between points B and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.86
|
math
|
geometry_polygon_train_0002
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFG is a regular 7-gon with center X and circumradius 12. Point K is obtained by rotating point X by angle pi/3 about point F. Let I be the midpoint of segment KG. Point J is the midpoint of segment EI. Let L be the line through points E and J. Let W be the midpoint of segment KX. Let U be the line through points G and W. Lines L and U intersect at point H. Point V is the midpoint of segment XD. Find the length of segment HV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.55
|
math
|
geometry_polygon_train_0003
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJK is a regular 11-gon with center R and circumradius 9. Let W be the reflection of point B across point D. Point P is the midpoint of segment AR. Point V is the midpoint of segment IP. Point Y is the reflection of point V across point R. What is the distance between points Y and W? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.04
|
math
|
geometry_polygon_train_0004
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center O and circumradius 6. Line Y is the angle bisector of angle EHG. Line M passes through point D parallel to line Y. Point Z is the intersection of segment CH and line M. Find the distance between points Z and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.39
|
math
|
geometry_polygon_train_0005
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDE be a regular 5-gon with center Z and circumradius 10. Let M be the circumcircle of polygon ABCDE. Point Q is the reflection of point Z across point D. Let R be the midpoint of segment BQ. Let I be the inversion of point R in circle M. What is the distance between points R and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8.42
|
math
|
geometry_polygon_train_0006
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHI is a regular 9-gon with center K and circumradius 10. Point Q is the reflection of point F across point B. Let L be the rotation of point I by angle 5pi/12 around point A. Let Y be the circumcircle of polygon ABCDEFGHI. Point V is the inversion of point Q with respect to circle Y. Let J be the perpendicular bisector of segment FL. Line Z passes through point F parallel to line J. Line S passes through point V parallel to line Z. Line S and segment FL intersect at point R. What is the distance between points R and F? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.11
|
math
|
geometry_polygon_train_0007
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "BCDEFGHI is a regular octagon with center A and circumradius 10. Point L is the midpoint of segment EG. Line M is the angle bisector of angle DGL. Point K is the reflection of point D across line M. Point J is the reflection of point K across point H. Point U is the midpoint of segment JL. What is the distance between points U and C? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23.85
|
math
|
geometry_polygon_train_0008
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 1. Point K is the reflection of point D across segment BC. Point I is the midpoint of segment KG. Point X is the midpoint of segment KC. Find the length of segment IX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.97
|
math
|
geometry_polygon_train_0009
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDFGHIJKL be a regular 11-gon with center E and circumradius 4. Let S be the circumcircle of polygon ABCDFGHIJKL. Line Z is the angle bisector of angle CKG. Line N is the perpendicular bisector of segment EJ. Let Y be the midpoint of segment AC. Let T be the reflection of line N across line Z. Circle X is the reflection of circle S across line T. Let M be the inversion of point Y in circle X. Find the length of segment MG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.71
|
math
|
geometry_polygon_train_0010
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center T and circumradius 4. Point X is the midpoint of segment DE. Let Q be the rotation of point D by angle pi/12 around point A. Let M be the angle bisector of angle TXQ. Let O be the reflection of line M through point F. Point I is the reflection of point B across line O. Point V is the intersection of segment XI and line O. What is the length of segment VA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.87
|
math
|
geometry_polygon_train_0011
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKL is a regular dodecagon with center R and circumradius 11. Let Z be the circumcircle of polygon ABCDEFGHIJKL. Let Q be the midpoint of segment IL. Let P be the inversion of point Q in circle Z. What is the distance between points Q and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.78
|
math
|
geometry_polygon_train_0012
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ACDEF is a regular 5-gon with center B and circumradius 2. Line J is the angle bisector of angle DBF. Let V be the reflection of line J through point A. Point T is the reflection of point C across point F. Line X passes through points T and C. Point M is the reflection of point C across line V. Point L is the reflection of point D across line X. Find the length of segment LM. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.33
|
math
|
geometry_polygon_train_0013
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 9. Point Y is obtained by rotating point A by angle pi/6 about point F. Line Q is the angle bisector of angle DLK. Let T be the reflection of line Q through point K. Point M is the reflection of point F across line T. Point O is the midpoint of segment MA. Find the length of segment OY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23.29
|
math
|
geometry_polygon_train_0014
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFG is a regular 7-gon with center R and circumradius 5. Line Z is the angle bisector of angle BCF. Line S passes through point R perpendicular to line Z. Point V is the reflection of point F across line S. Point X is the midpoint of segment RD. Point I is the midpoint of segment VX. What is the distance between points I and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.48
|
math
|
geometry_polygon_train_0015
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Q and circumradius 1. Let R be the perpendicular bisector of segment QE. Line T is the reflection of line R across point A. Line S is the reflection of line T across point J. Line S and segment DJ intersect at point X. What is the length of segment XC? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.24
|
math
|
geometry_polygon_train_0016
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "BCDEFG is a regular hexagon with center A and circumradius 2. Point L is the midpoint of segment BF. Line N is the perpendicular bisector of segment LE. Point I is the reflection of point B across line N. Find the length of segment AI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.09
|
math
|
geometry_polygon_train_0017
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ACDEFGHI is a regular octagon with center B and circumradius 9. Let K be the midpoint of segment HI. Point O is the reflection of point K across point G. Point L is the midpoint of segment BI. Point T is the midpoint of segment LD. Find the length of segment OT. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19.22
|
math
|
geometry_polygon_train_0018
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center W and circumradius 4. Let X be the rotation of point G by angle 7pi/12 around point B. Let U be the line through point I parallel to segment FL. Let T be the circumcircle of polygon ABCDEFGHIJKL. Line Z passes through point A parallel to segment FL. Let V be the reflection of line U through point W. Let M be the reflection of circle T across line V. Circle R is the reflection of circle M across line Z. Point Y is the inversion of point X with respect to circle R. What is the length of segment YA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.67
|
math
|
geometry_polygon_train_0019
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJLM is a regular dodecagon with center K and circumradius 3. Point Z is the reflection of point M across point H. Let R be the line through points L and H. Let Q be the midpoint of segment ZA. Point N is the reflection of point G across line R. Find the length of segment NQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.26
|
math
|
geometry_polygon_train_0020
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center M and circumradius 9. Line Y is the angle bisector of angle LAD. Let W be the perpendicular bisector of segment CE. Let X be the reflection of line Y across line W. Line V passes through point M parallel to line Y. Point O is the intersection of lines V and X. Find the length of segment DO. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11.15
|
math
|
geometry_polygon_train_0021
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABDEFGHI is a regular octagon with center C and circumradius 5. Let M be the perpendicular bisector of segment AF. Point N is the reflection of point F across point E. Point V is the reflection of point N across line M. Find the length of segment CV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.37
|
math
|
geometry_polygon_train_0022
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 8. Point U is the reflection of point C across segment MG. Segments GJ and IL intersect at point Q. Let X be the perpendicular bisector of segment AL. Point O is the reflection of point Q across line X. What is the distance between points O and U? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.86
|
math
|
geometry_polygon_train_0023
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDE is a regular 5-gon with center N and circumradius 8. Line G passes through points A and C. Let V be the line through point D parallel to line G. Line Y is the reflection of line G across line V. Let U be the line through points B and N. Let S be the reflection of line Y through point N. Point R is the intersection of lines S and U. Find the measure of angle DNR, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.51
|
math
|
geometry_polygon_train_0024
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center T and circumradius 9. Point M is the midpoint of segment HB. Point X is the midpoint of segment GE. Line P passes through point X perpendicular to segment DH. Line L is the reflection of line P across point E. Point Q is the reflection of point M across line L. Find the length of segment QF. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
32.86
|
math
|
geometry_polygon_train_0025
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center X and circumradius 4. Let Y be the line through points B and K. Line Z is the reflection of line Y across point C. Point U is the intersection of line Z and segment HB. What is the distance between points U and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.07
|
math
|
geometry_polygon_train_0026
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 6. Point H is the midpoint of segment YE. Point N is obtained by rotating point H by angle pi/2 about point A. Point V is the midpoint of segment NB. Let P be the midpoint of segment DN. Point R is the reflection of point V across point C. Find the distance between points R and P. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20.14
|
math
|
geometry_polygon_train_0027
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center I and circumradius 4. Point J is the reflection of point D across point C. Let R be the circumcircle of polygon ABCDEF. Point V is the inversion of point J with respect to circle R. Let H be the reflection of point I across point C. Find the measure of angle HBV, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.05
|
math
|
geometry_polygon_train_0028
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFG is a regular 7-gon with center U and circumradius 11. Line W passes through points C and B. Point N is the reflection of point G across segment BF. Point L is the reflection of point A across line W. Find the length of segment LN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
26.75
|
math
|
geometry_polygon_train_0029
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center J and circumradius 10. Let U be the rotation of point C by angle 11pi/12 around point F. Point X is the midpoint of segment DB. Point W is the midpoint of segment FU. What is the length of segment WX? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24.94
|
math
|
geometry_polygon_train_0030
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center R and circumradius 12. Let N be the rotation of point D by angle 2pi/3 around point F. Point V is the reflection of point K across segment ND. Let S be the angle bisector of angle LVK. Point O is the reflection of point L across line S. What is the distance between points I and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.7
|
math
|
geometry_polygon_train_0031
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 12. Line V passes through points H and C. Line S is the angle bisector of angle FJB. Line M is the reflection of line S across line V. Point P is the reflection of point F across line M. Let Q be the reflection of point P across point G. Find the length of segment AQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
35.9
|
math
|
geometry_polygon_train_0032
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGH be a regular octagon with center W and circumradius 7. Point O is the midpoint of segment WD. Point K is the reflection of point O across segment WA. Let Z be the perpendicular bisector of segment WA. Point V is the reflection of point C across line Z. Find the length of segment VK. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.4
|
math
|
geometry_polygon_train_0033
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJ is a regular 10-gon with center Z and circumradius 11. Let L be the circumcircle of polygon ABCDEFGHIJ. Circle Q is the reflection of circle L across point I. Point X is the inversion of point G with respect to circle Q. Point M is the reflection of point B across point H. What is the length of segment XM? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
21.02
|
math
|
geometry_polygon_train_0034
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCD be a square with center P and circumradius 12. Let R be the circumcircle of polygon ABCD. Line Z is the angle bisector of angle DAP. Line N is the perpendicular bisector of segment BP. Let I be the reflection of circle R across line Z. Let H be the reflection of circle I across line N. Let S be the perpendicular bisector of segment AP. Point T is the inversion of point C with respect to circle H. Point L is the reflection of point T across line S. What is the distance between points T and L? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11.74
|
math
|
geometry_polygon_train_0035
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKL is a regular dodecagon with center T and circumradius 6. Point U is obtained by rotating point H by angle pi/6 about point B. Let W be the angle bisector of angle UDJ. Let Z be the perpendicular bisector of segment DC. Let N be the reflection of line W across line Z. Let P be the line through point U parallel to line N. Point X is the reflection of point K across line P. What is the distance between points D and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9.07
|
math
|
geometry_polygon_train_0036
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "BCDEFG is a regular hexagon with center A and circumradius 10. Line H passes through points D and A. Let L be the reflection of line H through point C. Let W be the reflection of line L across line H. Let O be the reflection of point E across point B. Point Y is the reflection of point O across line W. Find the distance between points E and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
55.68
|
math
|
geometry_polygon_train_0037
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABDEFGHI is a regular octagon with center C and circumradius 8. Point Y is the reflection of point H across point D. Let K be the midpoint of segment FD. Point Z is the midpoint of segment GY. Let Q be the reflection of point A across point Z. What is the length of segment KQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17.29
|
math
|
geometry_polygon_train_0038
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGH be a regular octagon with center P and circumradius 7. Line I is the angle bisector of angle PDH. Line M passes through points E and C. Point V is the reflection of point F across line M. Point N is the reflection of point V across line I. What is the distance between points N and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14.0
|
math
|
geometry_polygon_train_0039
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 8. Line Y is the perpendicular bisector of segment LK. Line X is the reflection of line Y across point A. Let R be the reflection of line X across line Y. Point Z is the reflection of point E across line X. Point S is the reflection of point F across line X. Line Q is the angle bisector of angle ZMS. Line P is the reflection of line R across line Q. Let V be the line through points I and C. Lines P and V intersect at point T. Find the length of segment ST. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
59.85
|
math
|
geometry_polygon_train_0040
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJ is a regular 10-gon with center M and circumradius 12. Let R be the reflection of point C across point F. Let Q be the midpoint of segment GF. Let P be the line through points Q and J. Segment DI and line P intersect at point Y. What is the length of segment YR? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
30.11
|
math
|
geometry_polygon_train_0041
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCD is a square with center O and circumradius 12. Point N is the reflection of point D across point B. Let Y be the perpendicular bisector of segment CA. Point M is the reflection of point D across segment AN. Point K is the reflection of point M across line Y. Let J be the midpoint of segment MK. Find the distance between points J and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.24
|
math
|
geometry_polygon_train_0042
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center T and circumradius 10. Let Q be the midpoint of segment LA. Let O be the line through point F parallel to segment GK. Point V is the reflection of point Q across line O. Find the length of segment VL. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.59
|
math
|
geometry_polygon_train_0043
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKL is a regular dodecagon with center R and circumradius 5. Let O be the perpendicular bisector of segment LR. Line U is the reflection of line O across point C. Let M be the circumcircle of polygon ABCDEFGHIJKL. Let N be the reflection of circle M across line U. Point X is the inversion of point J with respect to circle N. Find the length of segment XG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.11
|
math
|
geometry_polygon_train_0044
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center S and circumradius 3. Let W be the circumcircle of polygon ABCDEFGHIJKL. Let Z be the angle bisector of angle HCD. Circle Y is the reflection of circle W across line Z. Line T is the perpendicular bisector of segment SK. Let P be the rotation of point D by angle 2pi/3 around point F. Circle N is the reflection of circle Y across line T. Point X is the midpoint of segment PJ. Let U be the inversion of point X in circle N. Point M is the reflection of point U across line Z. Find the distance between points M and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.28
|
math
|
geometry_polygon_train_0045
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDFGHIJ be a regular 9-gon with center E and circumradius 10. Let N be the rotation of point A by angle 11pi/12 around point J. Point L is the reflection of point B across point N. Let S be the angle bisector of angle GCJ. Point Y is the reflection of point L across line S. Point Z is the reflection of point H across point Y. Find the length of segment ZI. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
42.57
|
math
|
geometry_polygon_train_0046
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "EM = 8. ABCDFGHIJKL is a regular 11-gon with center M and circumradius 7. Line O is the perpendicular bisector of segment JI. Point Z is the midpoint of segment GC. Line T passes through point D perpendicular to line O. Line V passes through point K perpendicular to line T. Point Y is the reflection of point Z across line V. Find the length of segment LY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
8.16
|
math
|
geometry_polygon_train_0047
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 8. Let L be the line through points G and I. Let T be the midpoint of segment BG. Point S is the reflection of point D across point F. Let Z be the perpendicular bisector of segment BT. Let V be the line through points S and F. Let Q be the reflection of line Z across line V. Lines L and Q intersect at point N. Point M is the midpoint of segment FE. What is the length of segment MN? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.39
|
math
|
geometry_polygon_train_0048
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDE be a regular 5-gon with center Q and circumradius 8. Let X be the reflection of point Q across point A. Let H be the angle bisector of angle QXB. Point O is the reflection of point C across line H. Let M be the midpoint of segment EO. What is the distance between points M and A? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9.72
|
math
|
geometry_polygon_train_0049
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center X and circumradius 2. Let Y be the line through points C and G. Line K passes through points H and X. Let S be the reflection of line Y through point E. Lines K and S intersect at point Q. What is the length of segment QA? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.21
|
math
|
geometry_polygon_train_0050
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center R and circumradius 1. Let J be the line through points B and D. Segment CF and line J intersect at point W. Let N be the midpoint of segment AW. Find the length of segment FN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.09
|
math
|
geometry_polygon_train_0051
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 5. Let Q be the circumcircle of polygon ABCDEFGIJKLM. Let X be the midpoint of segment MJ. Let S be the reflection of circle Q through point D. Point R is the reflection of point K across point X. Let Z be the inversion of point E in circle S. Point N is the reflection of point F across segment RK. What is the length of segment NZ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.29
|
math
|
geometry_polygon_train_0052
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCD be a square with center Q and circumradius 9. Let Z be the circumcircle of polygon ABCD. Let O be the midpoint of segment BA. Let V be the reflection of circle Z through point B. Point W is the inversion of point O with respect to circle V. Point M is the reflection of point W across point A. What is the distance between points M and D? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16.6
|
math
|
geometry_polygon_train_0053
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let BCDEFGHI be a regular octagon with center A and circumradius 3. Point U is the reflection of point C across point I. Let K be the midpoint of segment FA. Let X be the line through point K parallel to segment BE. Point P is the reflection of point H across line X. Find the length of segment UP. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.44
|
math
|
geometry_polygon_train_0054
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCEF is a regular 5-gon with center D and circumradius 2. Let K be the rotation of point B by angle 11pi/12 around point C. Point M is the reflection of point C across point K. Point T is the reflection of point F across point E. Point O is the reflection of point M across segment DK. What is the length of segment TO? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.47
|
math
|
geometry_polygon_train_0055
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDE be a regular 5-gon with center U and circumradius 10. Line Z passes through points D and C. Let X be the line through point E parallel to line Z. Line Q is the reflection of line X across line Z. Point G is the midpoint of segment CD. Point V is the reflection of point G across line Q. Find the length of segment VC. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
23.12
|
math
|
geometry_polygon_train_0056
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 11. Let X be the reflection of point K across point J. Let Z be the perpendicular bisector of segment IK. Line R passes through points M and X. Let Y be the reflection of line R across line Z. Point S is the reflection of point X across line Y. Find the distance between points A and S. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
10.2
|
math
|
geometry_polygon_train_0057
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJK be a regular 11-gon with center Q and circumradius 8. Line N is the perpendicular bisector of segment GF. Line O is the angle bisector of angle JQA. Let P be the line through point I parallel to line O. Line Z passes through point C parallel to line P. Let L be the reflection of line Z across line N. Lines Z and L intersect at point U. What is the measure of angle UQG, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2.86
|
math
|
geometry_polygon_train_0058
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center Q and circumradius 8. Line Z is the angle bisector of angle DFE. Let L be the perpendicular bisector of segment DE. Let Y be the rotation of point F by angle pi/12 around point A. Let I be the reflection of line Z across line L. Let R be the reflection of line L across line I. Point J is the reflection of point E across point D. Line V passes through point D parallel to line R. Let G be the angle bisector of angle DJF. Let O be the line through point Y parallel to line G. Point K is the intersection of lines V and O. What is the distance between points E and K? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
43.06
|
math
|
geometry_polygon_train_0059
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center S and circumradius 9. Line T is the angle bisector of angle CAF. Point U is the reflection of point H across line T. Let Z be the circumcircle of polygon ABCDEFGH. Circle L is the reflection of circle Z across point U. Point X is the inversion of point E with respect to circle L. Find the distance between points X and A. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14.2
|
math
|
geometry_polygon_train_0060
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFG be a regular 7-gon with center Q and circumradius 9. Let M be the circumcircle of polygon ABCDEFG. Let P be the reflection of circle M through point F. Point H is the inversion of point A with respect to circle P. Point J is the inversion of point G with respect to circle P. Point T is the reflection of point J across point G. Find the length of segment TH. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19.12
|
math
|
geometry_polygon_train_0061
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFG be a regular 7-gon with center P and circumradius 10. Point O is obtained by rotating point C by angle pi about point B. Line R passes through point C perpendicular to segment CG. Line Y passes through point E parallel to line R. Let Q be the circumcircle of polygon ABCDEFG. Let W be the inversion of point O in circle Q. Let H be the reflection of circle Q through point W. Line L passes through points D and P. Point U is the reflection of point A across point G. Let I be the reflection of line Y across line L. Circle Z is the reflection of circle H across line I. Let S be the inversion of point U in circle Z. Find the distance between points S and U. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
16.38
|
math
|
geometry_polygon_train_0062
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJ is a regular 10-gon with center Y and circumradius 4. Let M be the circumcircle of polygon ABCDEFGHIJ. Circle V is the reflection of circle M across point G. Let N be the reflection of point C across point B. Point L is the inversion of point N with respect to circle V. What is the length of segment IL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.61
|
math
|
geometry_polygon_train_0063
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 4. Let U be the perpendicular bisector of segment CD. Line T is the reflection of line U across point D. Let N be the line through point I perpendicular to line T. Point Q is the reflection of point A across line N. Find the measure of angle BQH, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
0.94
|
math
|
geometry_polygon_train_0064
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCD be a square with center W and circumradius 10. Line H is the angle bisector of angle DBW. Line Y passes through points W and A. Line N passes through point A parallel to line H. Point U is the midpoint of segment WC. Point F is the reflection of point B across line N. Point M is the reflection of point F across line Y. What is the distance between points U and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
26.93
|
math
|
geometry_polygon_train_0065
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center I and circumradius 8. Line P is the perpendicular bisector of segment CI. Point Q is the reflection of point D across line P. Let N be the midpoint of segment DQ. Point R is the midpoint of segment QC. Find the length of segment RN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3.06
|
math
|
geometry_polygon_train_0066
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "BCDEFGHIJKLM is a regular dodecagon with center A and circumradius 12. Let S be the line through points M and J. Line Z is the perpendicular bisector of segment GF. Let T be the reflection of line Z through point E. Lines S and T intersect at point Y. What is the distance between points F and Y? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
34.13
|
math
|
geometry_polygon_train_0067
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center W and circumradius 12. Point N is on segment EG. Let Y be the perpendicular bisector of segment GB. Point L is the reflection of point N across line Y. What is the measure of angle ENL, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.18
|
math
|
geometry_polygon_train_0068
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center X and circumradius 10. Let S be the angle bisector of angle XHE. Let J be the midpoint of segment FA. Point N is the reflection of point X across line S. Point T is the midpoint of segment NJ. Find the distance between points T and C. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.39
|
math
|
geometry_polygon_train_0069
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDE is a regular 5-gon with center G and circumradius 11. Let F be the rotation of point A by angle pi/3 around point G. Point K is the midpoint of segment DF. Point X is the reflection of point B across point K. Point O is the midpoint of segment FX. Point H is the reflection of point O across point X. What is the length of segment KH? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20.71
|
math
|
geometry_polygon_train_0070
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCD is a square with center W and circumradius 9. Let I be the circumcircle of polygon ABCD. Let T be the reflection of circle I through point D. Let X be the midpoint of segment WB. Point G is the inversion of point X with respect to circle T. Find the length of segment GW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14.4
|
math
|
geometry_polygon_train_0071
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHJK be a regular 10-gon with center I and circumradius 4. Line O passes through points H and B. Let P be the line through point K parallel to segment JE. Lines P and O intersect at point S. What is the length of segment SG? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.31
|
math
|
geometry_polygon_train_0072
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHI is a regular 9-gon with center S and circumradius 11. Let N be the perpendicular bisector of segment ID. Point M is the midpoint of segment CD. Let X be the line through point M parallel to line N. Segment ID and line X intersect at point Y. Find the distance between points Y and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
17.65
|
math
|
geometry_polygon_train_0073
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 7. Let Z be the midpoint of segment DC. Point V is the reflection of point Z across segment MF. Find the length of segment ZV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.06
|
math
|
geometry_polygon_train_0074
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFG is a regular 7-gon with center R and circumradius 11. Let O be the line through points A and C. Point Y is the reflection of point F across line O. Point V is the reflection of point Y across segment BC. What is the distance between points V and B? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.5
|
math
|
geometry_polygon_train_0075
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 10. Point Y is the reflection of point G across point E. Let P be the midpoint of segment XA. Point S is obtained by rotating point P by angle 3pi/4 about point F. Point M is the reflection of point E across point P. Line R passes through points M and J. Let Z be the line through point Y parallel to line R. Let V be the reflection of line Z through point D. Let N be the midpoint of segment SL. Point T is the reflection of point N across line V. What is the distance between points T and I? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.44
|
math
|
geometry_polygon_train_0076
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 2. Let X be the line through points I and G. Let Q be the angle bisector of angle KFM. Let Y be the reflection of line X across line Q. Point R is the reflection of point G across line Y. What is the distance between points M and R? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.29
|
math
|
geometry_polygon_train_0077
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 11. Let K be the circumcircle of polygon ABCDEFGH. Let Z be the reflection of circle K through point B. Point J is the midpoint of segment FA. Point Q is the inversion of point I with respect to circle Z. Point O is the midpoint of segment CJ. What is the distance between points O and Q? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
13.56
|
math
|
geometry_polygon_train_0078
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDFGHI is a regular octagon with center E and circumradius 3. Line R passes through points C and D. Line Y passes through point G parallel to segment HF. Point P is the intersection of lines R and Y. What is the length of segment HP? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.42
|
math
|
geometry_polygon_train_0079
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFG is a regular 7-gon with center Y and circumradius 4. Line K is the perpendicular bisector of segment YF. Point I is the reflection of point C across line K. Let U be the line through points G and A. Let W be the line through point I perpendicular to line U. Point O is the reflection of point Y across line W. Find the distance between points O and Y. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.6
|
math
|
geometry_polygon_train_0080
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHI is a regular 9-gon with center Z and circumradius 5. Line P passes through point B perpendicular to segment GE. Point M lies on line P. Let W be the reflection of point F across point D. Find the measure of angle WBM, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.4
|
math
|
geometry_polygon_train_0081
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJK be a regular 11-gon with center T and circumradius 7. Let N be the perpendicular bisector of segment FI. Point Z is the reflection of point A across point C. Line R is the reflection of line N across point I. Line U is the perpendicular bisector of segment IJ. Line L is the reflection of line U across line R. Line P passes through points H and Z. Point Q is the intersection of lines L and P. Find the length of segment BQ. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.48
|
math
|
geometry_polygon_train_0082
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEF is a regular hexagon with center L and circumradius 12. Let K be the circumcircle of polygon ABCDEF. Point O is the midpoint of segment FL. Let H be the inversion of point O in circle K. Point R is the reflection of point L across point C. What is the distance between points R and H? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
48.0
|
math
|
geometry_polygon_train_0083
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGIJK is a regular 10-gon with center H and circumradius 10. Line V is the angle bisector of angle GEI. Let U be the midpoint of segment BD. Let P be the line through point F perpendicular to line V. Point X is the reflection of point U across line P. Find the length of segment XE. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.48
|
math
|
geometry_polygon_train_0084
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 2. Point R is obtained by rotating point A by angle pi/12 about point G. Point W is obtained by rotating point B by angle pi/12 about point A. Let T be the circumcircle of polygon ABDEFG. Let O be the perpendicular bisector of segment CA. Line L passes through points R and E. Let J be the reflection of circle T across line L. Point H is the inversion of point C with respect to circle J. Point U is the reflection of point W across line O. What is the length of segment HU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
18.8
|
math
|
geometry_polygon_train_0085
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDE is a regular 5-gon with center R and circumradius 9. Let U be the circumcircle of polygon ABCDE. Let M be the reflection of circle U through point A. Let J be the perpendicular bisector of segment RB. Let T be the reflection of circle M across line J. Point L is the midpoint of segment EA. Point S is the inversion of point A with respect to circle T. Find the distance between points S and L. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.03
|
math
|
geometry_polygon_train_0086
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 5. Let O be the reflection of point C across point A. Let Q be the perpendicular bisector of segment OY. Line R is the reflection of line Q across point F. Let V be the line through point Y parallel to line R. Point M is the intersection of segment DB and line V. What is the distance between points O and M? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
11.86
|
math
|
geometry_polygon_train_0087
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEF is a regular hexagon with center Z and circumradius 11. Line S is the angle bisector of angle ACB. Let M be the circumcircle of polygon ABCDEF. Let U be the reflection of circle M across line S. Let N be the inversion of point F in circle U. Find the length of segment NF. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
19.68
|
math
|
geometry_polygon_train_0088
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center S and circumradius 10. Line Q passes through point C parallel to segment FJ. Point Z is the reflection of point L across line Q. Point P is the midpoint of segment EZ. What is the distance between points K and P? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.32
|
math
|
geometry_polygon_train_0089
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEFGH be a regular octagon with center R and circumradius 10. Line Y is the perpendicular bisector of segment CB. Let W be the line through point F parallel to line Y. Point U is the intersection of line W and segment AE. Find the distance between points U and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
7.65
|
math
|
geometry_polygon_train_0090
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDE be a regular 5-gon with center X and circumradius 12. Let N be the line through points B and E. Let J be the line through point X parallel to line N. Point I is the midpoint of segment AC. Let U be the line through point D parallel to line J. Let H be the reflection of line J across line U. Point Y is the reflection of point I across line H. Find the length of segment EY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
46.17
|
math
|
geometry_polygon_train_0091
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCEF is a regular 5-gon with center D and circumradius 10. Point T is the reflection of point B across point D. Line N is the perpendicular bisector of segment TB. Point M is the reflection of point C across segment BA. Let Z be the line through point F perpendicular to line N. Point J is the reflection of point C across line Z. What is the measure of angle JAM, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1.89
|
math
|
geometry_polygon_train_0092
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 4. Let H be the circumcircle of polygon ABCDEF. Let P be the midpoint of segment DL. Point I is the inversion of point P with respect to circle H. Point V is the midpoint of segment CD. What is the distance between points I and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
5.29
|
math
|
geometry_polygon_train_0093
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGHIJKL is a regular dodecagon with center X and circumradius 5. Let S be the reflection of point K across point C. Let O be the angle bisector of angle SGE. Line T is the reflection of line O across point J. Point N is the reflection of point E across line T. Find the distance between points I and N. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
24.18
|
math
|
geometry_polygon_train_0094
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFGH is a regular octagon with center L and circumradius 3. Let N be the line through point E perpendicular to segment BE. Point T is the reflection of point G across segment BE. Point X is the reflection of point T across line N. Find the length of segment LX. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
6.71
|
math
|
geometry_polygon_train_0095
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDFGHIJK be a regular 10-gon with center E and circumradius 9. Let V be the reflection of point I across point B. Let T be the perpendicular bisector of segment EV. Let U be the angle bisector of angle CIV. Let Q be the reflection of line T through point I. Let Z be the reflection of line U through point C. Lines Q and Z intersect at point L. Find the distance between points L and G. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
25.45
|
math
|
geometry_polygon_train_0096
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 9. Point L is the reflection of point M across point A. Point G is the reflection of point B across point F. Let N be the midpoint of segment GL. Let X be the midpoint of segment EM. What is the distance between points N and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
15.59
|
math
|
geometry_polygon_train_0097
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "ABCDEFG is a regular 7-gon with center I and circumradius 9. Let T be the perpendicular bisector of segment ID. Line M is the reflection of line T across point E. Let Y be the circumcircle of polygon ABCDEFG. Let Z be the reflection of circle Y through point C. Let N be the midpoint of segment IC. Point L is the reflection of point C across segment ND. Line M and segment ND intersect at point R. Let J be the inversion of point L in circle Z. What is the distance between points R and J? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
9.23
|
math
|
geometry_polygon_train_0098
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDEF be a regular hexagon with center P and circumradius 7. Point Q is the reflection of point D across point C. Let T be the reflection of point Q across point E. Let I be the midpoint of segment CQ. Point V is the reflection of point P across segment IT. Find the distance between points V and Q. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
12.76
|
math
|
geometry_polygon_train_0099
|
geometry_polygon
| null |
[
{
"role": "user",
"content": "Let ABCDE be a regular 5-gon with center S and circumradius 9. Let J be the angle bisector of angle CDE. Line O is the perpendicular bisector of segment EB. Line M is the reflection of line J across line O. Point U is the reflection of point B across point C. Let Q be the line through point E parallel to segment CA. Lines Q and M intersect at point R. What is the length of segment RU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
39.71
|
math
|
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