messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
value |
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[
{
"content": "ABCD is a square with center N and circumradius 9. Line Q is the perpendicular bisector of segment DC. Line J is the reflection of line Q across point D. Point T is obtained by rotating point N by angle 5pi/6 about point A. Point H is the reflection of point T across line J. Let P be the line thro... | 14.88 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 1. Let W be the circumcircle of polygon ABCDEF. Point Q is the midpoint of segment DF. Point V is the inversion of point Q with respect to circle W. Point O is the reflection of point B across point F. What is the length of segment VO? Exp... | 1.73 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center R and circumradius 7. Line Y is the perpendicular bisector of segment ER. Let O be the midpoint of segment AR. Let K be the line through point D parallel to line Y. Point J is the reflection of point O across line K. Let T be the midpoint of segment OD. Let... | 6.66 | MATH |
[
{
"content": "Let ABCD be a square with center Z and circumradius 12. Let X be the angle bisector of angle DBC. Point Q is the midpoint of segment DC. Line O is the perpendicular bisector of segment CQ. Point J is the reflection of point Z across line O. Point W is the reflection of point A across line X. What ... | 12.5 | MATH |
[
{
"content": "Let ACDE be a square with center B and circumradius 10. Let W be the rotation of point E by angle 2pi/3 around point A. Let X be the circumcircle of polygon ACDE. Let K be the line through points D and B. Let Y be the line through points C and W. Let J be the midpoint of segment DE. Let Q be the r... | 29.09 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center N and circumradius 6. Let W be the rotation of point E by angle pi/2 around point B. Let Z be the perpendicular bisector of segment CW. Let S be the line through point N parallel to line Z. Line M passes through points C and E. Let H be the reflection of line S... | 3.17 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center O and circumradius 4. Line Z passes through point D perpendicular to segment OI. Let N be the line through point H parallel to line Z. Point Q is the reflection of point G across line N. What is the measure of angle ACQ, in radians? Express your answer as... | 0.94 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 7. Let Q be the circumcircle of polygon ABCDEF. Point X is obtained by rotating point J by angle pi/12 about point F. Point M is the reflection of point E across segment CB. Point H is the inversion of point X with respect to circle Q. Poi... | 18.77 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center V and circumradius 6. Let Y be the circumcircle of polygon ABCDEF. Let K be the reflection of circle Y through point B. Point H is the reflection of point E across point A. Let M be the reflection of circle K through point H. Point Q is the inversion of poin... | 9.44 | MATH |
[
{
"content": "ACDEFGH is a regular 7-gon with center B and circumradius 10. Line Y is the perpendicular bisector of segment GB. Let Q be the circumcircle of polygon ACDEFGH. Let V be the reflection of circle Q through point E. Point R is the reflection of point A across line Y. Point W is the inversion of point... | 28.92 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center N and circumradius 4. Point V is the midpoint of segment CE. Let Y be the reflection of point F across point E. Point K is the reflection of point N across point D. Point R is the reflection of point K across point E. Line M passes through points V and F. ... | 3.45 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 3. Let G be the reflection of point E across point C. Point S is the reflection of point G across segment DE. Point Z is the reflection of point S across point D. Point W is the reflection of point Z across segment DE. What is the length o... | 6.0 | MATH |
[
{
"content": "Let ABCD be a square with center H and circumradius 3. Line Y is the perpendicular bisector of segment AB. Let I be the line through point D perpendicular to line Y. Point V is the reflection of point H across line I. Point O is the reflection of point H across segment BV. Point J is the midpoint ... | 3.16 | MATH |
[
{
"content": "Let ABCDEFGIJKLM be a regular dodecagon with center H and circumradius 7. Let P be the line through points E and G. Let N be the line through point A parallel to line P. Let Z be the midpoint of segment LK. Point Q is the reflection of point Z across line N. What is the length of segment KQ? Expre... | 4.05 | MATH |
[
{
"content": "Let ABCD be a square with center T and circumradius 11. Line O passes through points T and A. Point F is the midpoint of segment AD. Point Y is the reflection of point B across point D. Point S is the reflection of point Y across line O. What is the length of segment SF? Express your answer as a d... | 38.89 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center P and circumradius 3. Let S be the midpoint of segment FB. Let M be the angle bisector of angle HAI. Let Q be the line through point C parallel to line M. Line R passes through point B perpendicular to line Q. Let Z be the line through point S perpend... | 2.71 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center U and circumradius 4. Let N be the circumcircle of polygon ABCDEF. Line L passes through points E and D. Let O be the line through point F perpendicular to line L. Circle W is the reflection of circle N across line O. Let I be the inversion of point D in cir... | 1.05 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center H and circumradius 10. Let X be the perpendicular bisector of segment HD. Let U be the reflection of line X through point E. Point W is the reflection of point H across line U. Point T is the midpoint of segment EC. Let N be the midpoint of segment WD. What... | 3.09 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center S and circumradius 7. Line I is the angle bisector of angle ACB. Line K is the reflection of line I across point S. Let V be the line through points B and C. Line G is the reflection of line K across line V. Point U is the reflection of point C across line G... | 25.24 | MATH |
[
{
"content": "Let ABCD be a square with center I and circumradius 2. Line O is the angle bisector of angle DCI. Let M be the reflection of line O through point A. Point G is the reflection of point D across line M. Let V be the reflection of point B across point D. Let J be the midpoint of segment CG. Point K i... | 6.42 | MATH |
[
{
"content": "ABCD is a square with center E and circumradius 11. Point F is the reflection of point A across point D. Point M is the reflection of point C across point B. Let W be the perpendicular bisector of segment BD. Let X be the line through point M parallel to line W. Point N is the reflection of point ... | 66.0 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 10. Let X be the midpoint of segment EA. Line J passes through point C parallel to segment FB. Point T is obtained by rotating point X by angle pi/2 about point D. Point M is the reflection of point A across point C. Point P is the reflection... | 24.52 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 1. Point Q is the reflection of point B across segment DF. Line Z is the perpendicular bisector of segment DB. Let T be the perpendicular bisector of segment FQ. Let R be the reflection of line Z across line T. Point H is the reflectio... | 3.61 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center M and circumradius 5. Let T be the angle bisector of angle AGB. Point X is the reflection of point C across line T. Point N is the reflection of point X across segment AF. Find the distance between points N and H. Express your answer as a decimal number ro... | 8.21 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center M and circumradius 4. Let U be the circumcircle of polygon ABCDEF. Line I is the perpendicular bisector of segment MF. Let W be the reflection of circle U across line I. Let O be the inversion of point C in circle W. Point R is the reflection of point D acro... | 5.29 | MATH |
[
{
"content": "ABCDEFH is a regular 7-gon with center G and circumradius 5. Let X be the rotation of point D by angle 3pi/4 around point B. Let O be the midpoint of segment XB. Let J be the angle bisector of angle FOA. Line M is the reflection of line J across point F. Point I is the reflection of point H across... | 1.87 | MATH |
[
{
"content": "Let ACDEF be a regular 5-gon with center B and circumradius 10. Point P is obtained by rotating point C by angle pi/3 about point A. Line W is the perpendicular bisector of segment FA. Point V is the reflection of point P across segment FA. Let Z be the line through point V parallel to line W. Poi... | 8.74 | MATH |
[
{
"content": "Let ABCDEFGHJKLM be a regular dodecagon with center I and circumradius 10. Line V passes through points E and C. Let U be the angle bisector of angle JDB. Line S is the reflection of line U across line V. Lines S and V intersect at point Z. Find the length of segment ZI. Express your answer as a d... | 8.68 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 8. Let U be the angle bisector of angle HAD. Point T is the reflection of point E across point D. Point R is the reflection of point T across line U. Line Y passes through point R parallel to segment GF. Line K passes through point A... | 22.63 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 12. Let R be the circumcircle of polygon ABCDEFGHIJKL. Let N be the midpoint of segment EJ. Let M be the reflection of circle R through point K. Point O is the reflection of point N across point L. Point Q is the inversion of point... | 12.56 | MATH |
[
{
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 6. Point Q is obtained by rotating point F by angle pi/12 about point E. Let Z be the angle bisector of angle BAE. Let T be the line through point Q perpendicular to line Z. Point H is the reflection of point C across line T. Line P is... | 5.36 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 7. Point Q is the midpoint of segment AC. Point R is the midpoint of segment QD. Point K is the midpoint of segment HF. What is the distance between points K and R? Express your answer as a decimal number rounded to 2 decimal places.... | 9.2 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center H and circumradius 6. Let J be the line through points E and C. Point R is the reflection of point F across line J. Point Y is the reflection of point G across segment CB. What is the measure of angle RYB, in radians? Express your answer as a decimal number r... | 0.45 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center R and circumradius 12. Line J passes through points B and D. Line P passes through point R perpendicular to segment FD. Let T be the reflection of line P across line J. Point Z is the intersection of lines J and T. Point L is the midpoint of segment FD. What ... | 41.11 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center U and circumradius 2. Let I be the reflection of point A across point C. Point Q is the reflection of point E across point I. Let J be the midpoint of segment ID. Line V passes through point Q perpendicular to segment CJ. Point Z is the reflection of poi... | 9.17 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 3. Let Q be the rotation of point B by angle 3pi/4 around point C. Point U is obtained by rotating point E by angle pi about point A. Let S be the rotation of point Q by angle 5pi/6 around point U. Let Z be the midpoint of segment AF. Let ... | 6.74 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 11. Point S is obtained by rotating point D by angle 5pi/6 about point C. Line I passes through point C perpendicular to segment BS. Line R passes through point A parallel to line I. Point N is the reflection of point C across line R. ... | 9.86 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center P and circumradius 4. Line N passes through points B and D. Point R is the intersection of segment FC and line N. Let M be the midpoint of segment PI. Find the length of segment MR. Express your answer as a decimal number rounded to 2 decimal places.\n\n... | 5.4 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center W and circumradius 1. Let M be the rotation of point C by angle 5pi/12 around point E. Let R be the perpendicular bisector of segment MF. Let J be the line through point W perpendicular to segment EB. Let S be the reflection of line J across line R. Line S a... | 0.44 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center H and circumradius 6. Point Q is the reflection of point A across point F. Let U be the reflection of point B across point Q. Let L be the circumcircle of polygon ABCDEF. Point P is the inversion of point U with respect to circle L. Find the length of segmen... | 6.0 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center W and circumradius 1. Point U is the reflection of point D across point W. Point O is the midpoint of segment CD. Let K be the line through points B and E. Point P is the reflection of point D across point U. Line R is the reflection of line K across point ... | 10.44 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center P and circumradius 3. Point V is the reflection of point F across point B. Line Q passes through points V and P. Point M is the reflection of point B across line Q. Point Y is the midpoint of segment PA. Find the length of segment MY. Express your answer... | 3.54 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 7. Let N be the reflection of point E across point A. Let K be the circumcircle of polygon ABCDEF. Line I is the angle bisector of angle MNC. Let X be the reflection of circle K across line I. Let G be the inversion of point F in circl... | 17.56 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center I and circumradius 11. Let T be the circumcircle of polygon ABCDEF. Let P be the reflection of circle T through point D. Point K is the inversion of point A with respect to circle P. Point J is the reflection of point B across point F. Find the distance ... | 37.21 | MATH |
[
{
"content": "Let ABCDEFHIJ be a regular 9-gon with center G and circumradius 10. Point Q is the midpoint of segment FG. Let L be the line through points I and E. Line X passes through point D perpendicular to line L. Point R is the reflection of point Q across line X. Point P is the reflection of point R acros... | 23.61 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center X and circumradius 7. Let V be the midpoint of segment XC. Point O is the reflection of point X across point F. Let Z be the circumcircle of polygon ABCDEFGHIJ. Let Q be the inversion of point V in circle Z. Let T be the reflection of point O across point... | 28.21 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 1. Let N be the angle bisector of angle GDJ. Point S is the reflection of point B across line N. Line O is the angle bisector of angle CSF. Point R is the reflection of point A across line O. Find the length of segment SR. Expr... | 2.33 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center O and circumradius 12. Let W be the circumcircle of polygon ABCDEFGHI. Line V passes through points C and D. Circle S is the reflection of circle W across line V. Point J is the inversion of point G with respect to circle S. Find the distance between points... | 24.07 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center S and circumradius 11. Let N be the midpoint of segment CA. Point M is the midpoint of segment CF. Line X passes through point E perpendicular to segment FN. Let P be the reflection of point H across point M. Point R is the reflection of point D across... | 14.58 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center F and circumradius 2. Let L be the rotation of point B by angle pi/6 around point A. Let G be the reflection of point B across point F. Let N be the vector from point B to point G. Line W is the perpendicular bisector of segment EC. Point V is the translati... | 8.74 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center R and circumradius 12. Point Z is the reflection of point A across segment GB. Let K be the angle bisector of angle BAZ. Point W is the reflection of point D across line K. What is the distance between points W and G? Express your answer as a decimal number r... | 29.45 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 3. Line T passes through points A and F. Let Q be the perpendicular bisector of segment EF. Let J be the midpoint of segment EF. Let Y be the circumcircle of polygon ABCDEF. Line R is the reflection of line T across line Q. Circle S is the... | 3.61 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center W and circumradius 4. Let Z be the midpoint of segment GW. Point L is the midpoint of segment ZE. Let T be the midpoint of segment AL. Let N be the reflection of point T across point G. What is the distance between points N and W? Express your answer as... | 8.36 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center O and circumradius 1. Point G is the reflection of point C across point B. Let L be the perpendicular bisector of segment AD. Line I passes through point G perpendicular to line L. Point N is the reflection of point E across line I. Find the measure of angl... | 0.31 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center R and circumradius 1. Point Z is the reflection of point D across point B. Let S be the circumcircle of polygon ABCDEFGHIJKL. Circle W is the reflection of circle S across point D. Let P be the inversion of point K in circle W. What is the length... | 2.36 | MATH |
[
{
"content": "Let ABCEFG be a regular hexagon with center D and circumradius 5. Let N be the line through points G and B. Line Z is the reflection of line N across point A. Point J is the reflection of point A across line Z. Let I be the reflection of point B across point J. Find the length of segment IJ. Expre... | 8.66 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center N and circumradius 12. Point K is the reflection of point A across point B. Let Y be the midpoint of segment AN. Point V is the midpoint of segment YK. Find the length of segment VD. Express your answer as a decimal number rounded to 2 decimal places.\n\... | 18.25 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 12. Let O be the midpoint of segment FD. Point Q is the reflection of point O across point B. Let M be the reflection of point E across point C. What is the length of segment MQ? Express your answer as a decimal number rounded to 2 decimal... | 21.63 | MATH |
[
{
"content": "ABCDEGHIJKLM is a regular dodecagon with center F and circumradius 12. Point X is the midpoint of segment KB. Let Z be the angle bisector of angle HXD. Point Q is the reflection of point C across line Z. Let U be the midpoint of segment GQ. What is the distance between points G and U? Express your... | 6.1 | MATH |
[
{
"content": "Let ABDEF be a regular 5-gon with center C and circumradius 10. Let Y be the circumcircle of polygon ABDEF. Point T is the midpoint of segment FE. Point V is the inversion of point T with respect to circle Y. Point W is the reflection of point V across point E. Find the distance between points T a... | 12.51 | MATH |
[
{
"content": "ABCDFGHIJKLM is a regular dodecagon with center E and circumradius 5. Let N be the midpoint of segment GD. Let Y be the line through point N perpendicular to segment NJ. Point P is the reflection of point H across line Y. What is the length of segment KP? Express your answer as a decimal number ro... | 13.56 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center W and circumradius 3. Line Q passes through points G and I. Point L is the reflection of point A across line Q. Let K be the midpoint of segment LW. What is the distance between points F and K? Express your answer as a decimal number rounded to 2 decimal pl... | 4.68 | MATH |
[
{
"content": "Let ABCEFGH be a regular 7-gon with center D and circumradius 10. Line N passes through points G and F. Let P be the circumcircle of polygon ABCEFGH. Circle L is the reflection of circle P across line N. Let X be the inversion of point E in circle L. Find the distance between points X and F. Expre... | 4.68 | MATH |
[
{
"content": "Let ABCDEFGIJKLM be a regular dodecagon with center H and circumradius 11. Let Q be the angle bisector of angle BHE. Point U is the midpoint of segment CB. Let V be the line through point D parallel to line Q. Let S be the reflection of point H across point U. Point R is the reflection of point L ... | 0.79 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center X and circumradius 4. Line I is the perpendicular bisector of segment FE. Line R is the reflection of line I across point G. Let H be the reflection of line R through point E. Point K is the reflection of point E across line H. Find the distance between point... | 17.12 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center T and circumradius 10. Point H is obtained by rotating point T by angle pi/12 about point A. Let I be the midpoint of segment FH. Line M is the perpendicular bisector of segment TF. Point L is the reflection of point C across line M. Let W be the reflection ... | 34.52 | MATH |
[
{
"content": "ABCDEG is a regular hexagon with center F and circumradius 8. Point W is the midpoint of segment BF. Let S be the midpoint of segment WD. Let H be the circumcircle of polygon ABCDEG. Point O is the inversion of point S with respect to circle H. Find the length of segment AO. Express your answer as... | 25.72 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 12. Let N be the line through point E perpendicular to segment FE. Let Z be the line through point F parallel to line N. Let O be the perpendicular bisector of segment FE. Point J is the reflection of point B across line Z. Point X is th... | 32.67 | MATH |
[
{
"content": "Let ABCD be a square with center R and circumradius 9. Point Z is the reflection of point A across point D. Point O is the midpoint of segment CZ. Let Y be the perpendicular bisector of segment RZ. Point H is the reflection of point O across line Y. Find the length of segment HA. Express your answ... | 17.08 | MATH |
[
{
"content": "ABCD is a square with center I and circumradius 12. Let E be the rotation of point D by angle 11pi/12 around point I. Point V is the reflection of point B across segment EC. Point L is the midpoint of segment EV. What is the distance between points L and E? Express your answer as a decimal number ... | 1.57 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center I and circumradius 3. Point Z is the reflection of point H across point A. Let R be the midpoint of segment DC. Line Q is the angle bisector of angle RBE. Point O is the reflection of point R across line Q. Point P is the reflection of point G across point... | 6.17 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 9. Point Y is the midpoint of segment DC. Let N be the midpoint of segment CI. Let W be the line through point I perpendicular to segment AF. Point J is the reflection of point Y across line W. What is the length of segment NJ? Express y... | 14.23 | MATH |
[
{
"content": "BCDEF is a regular 5-gon with center A and circumradius 1. Line I passes through point E perpendicular to segment BD. Point R is the reflection of point A across line I. Let Y be the midpoint of segment BD. Find the distance between points R and Y. Express your answer as a decimal number rounded t... | 1.22 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center M and circumradius 5. Line X is the angle bisector of angle CEM. Point J is the reflection of point M across line X. Let W be the line through points A and J. Point S is the reflection of point M across line W. Find the distance between points J and S. Expre... | 2.59 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center R and circumradius 4. Let Q be the rotation of point H by angle 5pi/12 around point A. Line O is the perpendicular bisector of segment EQ. Point Y is the reflection of point D across line O. Let X be the perpendicular bisector of segment YA. Point T is th... | 2.47 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center R and circumradius 2. Let X be the midpoint of segment GA. Let O be the perpendicular bisector of segment HD. Point U is the reflection of point X across line O. Find the length of segment CU. Express your answer as a decimal number rounded to 2 decima... | 1.41 | MATH |
[
{
"content": "ABCDEFHIJKLM is a regular dodecagon with center G and circumradius 4. Line O is the angle bisector of angle FIH. Point Q is the reflection of point D across line O. Let T be the midpoint of segment JQ. What is the measure of angle TJF, in radians? Express your answer as a decimal number rounded to... | 0.52 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center P and circumradius 12. Let Y be the angle bisector of angle DBE. Let T be the rotation of point G by angle 2pi/3 around point H. Let Q be the line through point P perpendicular to segment GB. Let W be the reflection of line Q across line Y. Point Z is the... | 36.66 | MATH |
[
{
"content": "Let ABDEFGHIJKL be a regular 11-gon with center C and circumradius 2. Line O is the angle bisector of angle DGE. Let S be the circumcircle of polygon ABDEFGHIJKL. Circle Y is the reflection of circle S across line O. Let R be the inversion of point K in circle Y. Find the distance between points R... | 1.45 | MATH |
[
{
"content": "ABCDEFGHIKLM is a regular dodecagon with center J and circumradius 4. Let U be the perpendicular bisector of segment CJ. Let P be the line through point L parallel to line U. Segment BI and line P intersect at point T. What is the measure of angle ITK, in radians? Express your answer as a decimal ... | 1.05 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center P and circumradius 1. Line W is the perpendicular bisector of segment CJ. Line T passes through points A and I. Line V is the reflection of line W across point I. Point U is the intersection of lines V and T. Let X be the midpoint of segment DA. What is t... | 2.99 | MATH |
[
{
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 5. Line S passes through point F parallel to segment ED. Let X be the midpoint of segment ED. Point N is the reflection of point X across line S. What is the length of segment EN? Express your answer as a decimal number rounded to 2 de... | 9.01 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 11. Let N be the angle bisector of angle DXG. Let V be the line through point D parallel to line N. Let J be the reflection of point A across point B. Point L is the reflection of point J across line V. Find the length of segment LG.... | 22.92 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center J and circumradius 8. Let L be the angle bisector of angle AJE. Let W be the line through point B parallel to line L. Let G be the circumcircle of polygon ABCDEF. Let I be the reflection of circle G across line W. Let M be the inversion of point J in cir... | 12.22 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 4. Let X be the line through points B and C. Line I passes through point C perpendicular to line X. Line P passes through point D parallel to line I. Let R be the circumcircle of polygon ABCDEFGH. Let W be the reflection of line P ac... | 6.49 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 2. Point J is obtained by rotating point G by angle 5pi/12 about point A. Point X is the reflection of point D across point H. Line U passes through point I perpendicular to segment BJ. Point W is the reflection of point B across lin... | 4.01 | MATH |
[
{
"content": "ABCEFGH is a regular 7-gon with center D and circumradius 5. Let R be the reflection of point G across point D. Let N be the line through points R and C. Point I lies on line N. Line U is the perpendicular bisector of segment AI. Point X is the reflection of point H across line U. Find the length ... | 4.34 | MATH |
[
{
"content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 3. Line V is the angle bisector of angle JLD. Line W passes through point E perpendicular to line V. Point Z is the reflection of point A across line W. Let T be the midpoint of segment KZ. What is the length of segment MT? Express... | 6.06 | MATH |
[
{
"content": "BCDEFGHIJK is a regular 10-gon with center A and circumradius 6. Let V be the midpoint of segment GF. Line W passes through points D and H. Line U passes through point V perpendicular to line W. Point S is the reflection of point D across line U. What is the distance between points A and S? Expres... | 9.42 | MATH |
[
{
"content": "ABCDEGHIJKLM is a regular dodecagon with center F and circumradius 3. Let X be the angle bisector of angle BMD. Line O passes through point G parallel to line X. Point Q is the reflection of point B across line O. Point T is the reflection of point Q across line X. Find the distance between points... | 13.57 | MATH |
[
{
"content": "Let ABCEFGHI be a regular octagon with center D and circumradius 2. Point N is the midpoint of segment FB. Let R be the line through point G parallel to segment AD. Line O passes through points C and E. Lines R and O intersect at point X. Find the length of segment NX. Express your answer as a dec... | 8.23 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center O and circumradius 12. Let Y be the angle bisector of angle HOE. Line S is the reflection of line Y across point H. Point W is the reflection of point I across line S. Let N be the reflection of point L across point A. What is the length of segment N... | 34.91 | MATH |
[
{
"content": "Let ABCDEFHIJ be a regular 9-gon with center G and circumradius 1. Point U is the reflection of point C across point B. Line O is the perpendicular bisector of segment HC. Line M is the perpendicular bisector of segment UD. Let S be the reflection of line M across line O. Line S and segment UD int... | 1.74 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center R and circumradius 7. Let W be the perpendicular bisector of segment JR. Line K is the angle bisector of angle JGR. Line T is the reflection of line W across line K. Let L be the reflection of line T through point I. Line U is the reflection of line L acr... | 20.09 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center M and circumradius 8. Let N be the perpendicular bisector of segment CB. Line O passes through point A parallel to line N. Let Y be the midpoint of segment AD. Point W is the reflection of point Y across point B. Point T is the reflection of point D across ... | 22.36 | MATH |
[
{
"content": "Let BCDEFGHIJKLM be a regular dodecagon with center A and circumradius 7. Point Z is the midpoint of segment GC. Let U be the midpoint of segment GZ. Let V be the midpoint of segment UK. Find the length of segment BV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ... | 8.69 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center T and circumradius 8. Let K be the circumcircle of polygon ABCDEFG. Circle P is the reflection of circle K across point A. Point S is the midpoint of segment CT. Point N is the inversion of point E with respect to circle P. Let I be the line through point... | 20.28 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center Q and circumradius 9. Point Z is the reflection of point C across point J. Point T is the midpoint of segment ZQ. Point S is the midpoint of segment QD. Find the length of segment ST. Express your answer as a decimal number rounded to 2 decimal places... | 15.65 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center W and circumradius 4. Line X passes through points D and H. Point P is obtained by rotating point K by angle 7pi/12 about point E. Let Q be the angle bisector of angle IWP. Line S passes through point C parallel to line X. Let Z be the reflection of ... | 2.01 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center P and circumradius 12. Point V is the reflection of point D across point G. Point K is the reflection of point G across point V. Let M be the midpoint of segment ED. Let O be the midpoint of segment PD. Point T is the reflection of point M across segment F... | 15.1 | MATH |
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