messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center N and circumradius 10. Let K be the line through points F and E. Let S be the line through point C parallel to line K. Let L be the reflection of line S across line K. Point T is the reflection of point F across line L. What is the measure of angle BFT, i... | 2.51 | MATH |
[
{
"content": "Let ABCDEFGI be a regular octagon with center H and circumradius 6. Let X be the midpoint of segment IB. Let W be the circumcircle of polygon ABCDEFGI. Let P be the inversion of point X in circle W. Line Q is the perpendicular bisector of segment PE. Let J be the reflection of circle W through poi... | 9.6 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center N and circumradius 12. Line I is the perpendicular bisector of segment NE. Let S be the midpoint of segment NC. Let T be the rotation of point S by angle pi/3 around point C. Line U passes through points S and D. Point R is the midpoint of segment SD. Le... | 30.46 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 10. Let X be the reflection of point F across point G. Let Z be the line through points H and X. Line S passes through point E perpendicular to line Z. Point K is the reflection of point F across line Z. Point N is the reflection of ... | 20.0 | MATH |
[
{
"content": "ABCDEFGI is a regular octagon with center H and circumradius 7. Point T is the reflection of point G across point I. Let L be the midpoint of segment BD. Point M is obtained by rotating point C by angle 3pi/4 about point D. Line O is the perpendicular bisector of segment MF. Point Q is the reflect... | 11.35 | MATH |
[
{
"content": "ABCDEGHIJKLM is a regular dodecagon with center F and circumradius 1. Line R is the angle bisector of angle DHI. Point W is the reflection of point F across line R. Line S passes through points I and E. Point X is the reflection of point L across line S. What is the distance between points X and W... | 2.13 | MATH |
[
{
"content": "ABCDEFGHIJLM is a regular dodecagon with center K and circumradius 7. Let N be the line through points A and K. Line R passes through point C parallel to line N. Line V is the reflection of line R across point H. Point T is the reflection of point L across line V. Find the distance between points ... | 15.65 | MATH |
[
{
"content": "Let ACDEF be a regular 5-gon with center B and circumradius 6. Line T passes through points B and F. Let V be the line through points A and D. Line Z passes through point D parallel to line T. Line L is the reflection of line Z across point B. Let M be the reflection of point D across point B. Poi... | 1.86 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center S and circumradius 1. Let T be the midpoint of segment BS. Let O be the perpendicular bisector of segment AT. Point X is the reflection of point B across line O. Let V be the midpoint of segment DX. Let Q be the reflection of point B across point V. Poin... | 0.5 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center K and circumradius 6. Line L is the angle bisector of angle FCG. Let X be the circumcircle of polygon ABCDEFGH. Let O be the reflection of circle X through point H. Let Q be the inversion of point A in circle O. Point U is the reflection of point E across ... | 4.93 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center R and circumradius 3. Let W be the reflection of point B across point R. Let K be the circumcircle of polygon ABCDE. Circle Y is the reflection of circle K across point C. Point Q is the inversion of point B with respect to circle Y. Let I be the perpendicu... | 2.44 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center S and circumradius 3. Let Q be the midpoint of segment BA. Point Y is the reflection of point G across point I. Let O be the line through point G parallel to segment BA. Point K is the reflection of point Y across line O. Find the distance between poi... | 12.49 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center R and circumradius 2. Let K be the rotation of point E by angle 2pi/3 around point G. Point Z is the midpoint of segment IB. Let P be the line through points E and Z. Line Y passes through point G parallel to line P. Point N is the reflection of point K a... | 4.05 | MATH |
[
{
"content": "ACDEFGHIJKLM is a regular dodecagon with center B and circumradius 1. Point T is the midpoint of segment JG. Let R be the midpoint of segment KT. Line V passes through point L parallel to segment GJ. Point N is the intersection of line V and segment RD. Find the measure of angle KHN, in radians. E... | 1.05 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center Z and circumradius 9. Point P is the reflection of point K across point I. Let X be the midpoint of segment ZK. Let L be the line through points X and P. Point U is the intersection of line L and segment JZ. What is the length of segment GU? Express ... | 10.53 | MATH |
[
{
"content": "Let BCDEFGHI be a regular octagon with center A and circumradius 7. Point N is the reflection of point H across point D. Line L is the angle bisector of angle ADC. Line O passes through point N parallel to line L. Point T is the reflection of point I across line O. What is the length of segment DT... | 22.09 | MATH |
[
{
"content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 7. Point Y is the reflection of point G across segment DI. Let V be the line through points A and G. Let X be the line through point Y parallel to segment EH. Point U is the reflection of point E across point M. Point W is the inte... | 23.61 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 5. Point S is the midpoint of segment AF. Let I be the midpoint of segment CD. Let G be the midpoint of segment AS. Point N is the midpoint of segment IO. Find the distance between points N and G. Express your answer as a decimal number ro... | 6.61 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 2. Line N passes through points I and H. Line P is the perpendicular bisector of segment AC. Let S be the reflection of line P across line N. Lines S and N intersect at point J. What is the distance between points J and H? Express your a... | 1.08 | MATH |
[
{
"content": "Let ABCDEFHIJK be a regular 10-gon with center G and circumradius 2. Let Z be the rotation of point B by angle pi/12 around point J. Line U is the angle bisector of angle EIK. Line X passes through point B parallel to line U. Point N lies on line X. Let S be the line through point N parallel to se... | 4.18 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center W and circumradius 8. Let T be the perpendicular bisector of segment BA. Let U be the line through points D and J. Line M is the reflection of line T across line U. Point O is the reflection of point G across line M. Find the length of segment JO. Exp... | 8.0 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center X and circumradius 3. Point M is the midpoint of segment CD. Point I is the midpoint of segment GM. Let N be the reflection of point C across point I. What is the length of segment EN? Express your answer as a decimal number rounded to 2 decimal places.\n\... | 3.95 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 3. Point X is the reflection of point C across point B. Let O be the perpendicular bisector of segment DL. Line K passes through point L perpendicular to line O. Point P is the midpoint of segment AC. Point J is the reflection of point... | 5.41 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center L and circumradius 9. Let V be the line through points H and A. Point Q is the reflection of point J across line V. Point P is the reflection of point C across line V. Point R is the reflection of point L across line V. Point M is the reflection of point... | 24.84 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 7. Let K be the midpoint of segment CB. Let P be the midpoint of segment CN. Let U be the reflection of point K across point B. Let W be the circumcircle of polygon ABCDEFGH. Let T be the inversion of point P in circle W. Let R be th... | 19.09 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center K and circumradius 8. Line P passes through points F and A. Point Y is the reflection of point H across line P. Let M be the midpoint of segment YK. What is the length of segment CM? Express your answer as a decimal number rounded to 2 decimal places.\n\nP... | 6.93 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center N and circumradius 2. Let T be the circumcircle of polygon ABCDEFG. Point S is the reflection of point E across point D. Let X be the midpoint of segment SD. Point R is the midpoint of segment CA. Let K be the inversion of point R in circle T. Find the le... | 3.88 | MATH |
[
{
"content": "JY = 2. ABCDEFGH is a regular octagon with center Y and circumradius 3. Let I be the circumcircle of polygon ABCDEFGH. Let T be the reflection of circle I through point F. Let O be the inversion of point G in circle T. Let S be the midpoint of segment AH. Find the distance between points O and S. ... | 5.51 | MATH |
[
{
"content": "Let ABCDEFGI be a regular octagon with center H and circumradius 12. Point W is the midpoint of segment CI. Let Q be the reflection of point H across point W. Let Z be the angle bisector of angle WEQ. Point K is the reflection of point A across line Z. Find the distance between points K and D. Exp... | 19.66 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 3. Line Z passes through points B and A. Let O be the circumcircle of polygon ACDEFGHI. Line T passes through point I parallel to line Z. Let P be the line through point H parallel to line T. Circle R is the reflection of circle O ac... | 3.08 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center R and circumradius 10. Let Q be the angle bisector of angle IFH. Let V be the circumcircle of polygon ABCDEFGHIJKL. Let Y be the reflection of circle V across line Q. Let O be the inversion of point R in circle Y. Find the length of segment OC. Expre... | 17.55 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 12. Point X is obtained by rotating point C by angle 7pi/12 about point F. Point W is the reflection of point A across point X. Let L be the reflection of point W across point B. Let J be the circumcircle of polygon ABCDF. Let P be the reflec... | 73.85 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center M and circumradius 2. Line P is the angle bisector of angle DCK. Let U be the midpoint of segment FK. Let Q be the reflection of point A across point H. Point X is the reflection of point Q across line P. What is the distance between points U and X? ... | 5.05 | MATH |
[
{
"content": "Let ABCDFGHI be a regular octagon with center E and circumradius 6. Point T is the reflection of point B across point D. Point V is obtained by rotating point T by angle 5pi/6 about point A. Let W be the rotation of point V by angle 3pi/4 around point G. Point L is the reflection of point E across... | 27.31 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center G and circumradius 11. Let M be the rotation of point B by angle pi/12 around point C. Line Z passes through point C perpendicular to segment CB. Line L passes through point D parallel to line Z. Let X be the midpoint of segment ME. Point S is the reflection of... | 34.63 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center L and circumradius 11. Point P is the midpoint of segment EL. Let W be the midpoint of segment DB. Point R is the midpoint of segment PA. Let X be the angle bisector of angle HFG. Point M is the reflection of point W across line X. What is the distance... | 26.79 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 9. Let Z be the angle bisector of angle MGH. Point T is the reflection of point L across line Z. Point U is the reflection of point T across segment ME. Let V be the midpoint of segment LC. Let P be the midpoint of segment UV. ... | 2.79 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Q and circumradius 7. Point H is obtained by rotating point B by angle pi about point A. Let P be the midpoint of segment DB. Point J is the midpoint of segment BP. Let Z be the perpendicular bisector of segment CH. Point N is the reflection of point J acro... | 8.62 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center V and circumradius 1. Let S be the angle bisector of angle BFV. Let U be the line through point H parallel to line S. Line P passes through point D parallel to line U. Point Q is the reflection of point F across line P. What is the distance between points B... | 2.56 | MATH |
[
{
"content": "Let ABCDFGHIJKLM be a regular dodecagon with center E and circumradius 3. Let O be the reflection of point H across point I. Let X be the midpoint of segment LK. Point Y is the reflection of point X across point O. Line V is the perpendicular bisector of segment LK. Point S is the reflection of po... | 3.06 | MATH |
[
{
"content": "BCDEFGHIJ is a regular 9-gon with center A and circumradius 1. Let V be the midpoint of segment IG. Line X passes through point D parallel to segment FA. Point M is the reflection of point V across line X. Find the length of segment CM. Express your answer as a decimal number rounded to 2 decimal ... | 1.96 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center J and circumradius 8. Let U be the midpoint of segment AB. Point Z is the midpoint of segment UC. Line K is the angle bisector of angle EDA. Point O is the reflection of point U across line K. Point P is the reflection of point O across segment BZ. Fin... | 24.92 | MATH |
[
{
"content": "Let ABCDEFGI be a regular octagon with center H and circumradius 9. Line L passes through points I and E. Point W is the reflection of point F across line L. Point P is the midpoint of segment WB. Find the length of segment PI. Express your answer as a decimal number rounded to 2 decimal places.\n... | 11.76 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center V and circumradius 8. Let O be the line through point B perpendicular to segment AB. Point H is the reflection of point V across line O. Point X is on segment AB. Find the measure of angle XBH, in radians. Express your answer as a decimal number rounded to ... | 2.2 | MATH |
[
{
"content": "Let ABCE be a square with center D and circumradius 7. Let I be the circumcircle of polygon ABCE. Line Z is the perpendicular bisector of segment BE. Line R passes through point B parallel to line Z. Let H be the reflection of circle I across line R. Point J is the inversion of point C with respec... | 11.29 | MATH |
[
{
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 11. Let Q be the reflection of point E across point D. Line P is the perpendicular bisector of segment FI. Line T passes through point J parallel to line P. Point V is the reflection of point L across line T. Let X be the midpo... | 24.19 | MATH |
[
{
"content": "Let ACDEFGHIJKLM be a regular dodecagon with center B and circumradius 7. Let Y be the line through points K and H. Line U passes through point D parallel to line Y. Let Z be the midpoint of segment GE. Let P be the reflection of line U through point Z. Let N be the circumcircle of polygon ACDEFGH... | 4.25 | MATH |
[
{
"content": "ABCDFGHIJKLM is a regular dodecagon with center E and circumradius 2. Line Y is the perpendicular bisector of segment KC. Let X be the line through point C parallel to line Y. Let P be the line through points E and J. Line Z is the reflection of line P across line X. Point Q is the reflection of p... | 0.52 | MATH |
[
{
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 9. Point R is the reflection of point F across point E. Let H be the reflection of point R across point C. Let X be the perpendicular bisector of segment HC. Let Z be the line through point E parallel to line X. Point N is the intersec... | 16.7 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center Y and circumradius 3. Line Q is the angle bisector of angle HGA. Let M be the line through point F perpendicular to line Q. Point T is the reflection of point Y across line M. Point R is the reflection of point T across line Q. Find the length of segment RY... | 7.49 | MATH |
[
{
"content": "ABCDEFGIJKL is a regular 11-gon with center H and circumradius 8. Let R be the angle bisector of angle CIA. Line V is the reflection of line R across point J. Let N be the midpoint of segment GL. Line X passes through point F parallel to line V. Let Y be the midpoint of segment GF. Let M be the mi... | 11.91 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center L and circumradius 9. Line O is the perpendicular bisector of segment GL. Let M be the line through point F parallel to line O. Line Y is the reflection of line O across line M. Point S is the reflection of point A across line Y. Find the length of seg... | 18.38 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 3. Line Y is the angle bisector of angle BPE. Let Z be the line through point A parallel to line Y. Point L is the midpoint of segment EP. Point H is the intersection of segment BL and line Z. What is the distance between points H and B? E... | 1.5 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 1. Point I is the reflection of point C across point G. Let M be the perpendicular bisector of segment XD. Point Q is the reflection of point F across line M. Let N be the midpoint of segment EI. Point S is the midpoint of segment NQ... | 2.45 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center O and circumradius 1. Let S be the circumcircle of polygon ABCDEFGHIJKL. Let Q be the reflection of circle S through point A. Line N is the perpendicular bisector of segment IH. Let W be the inversion of point F in circle Q. Let Z be the line through... | 2.89 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center V and circumradius 2. Let Z be the angle bisector of angle EDC. Line G is the angle bisector of angle ECV. Point M is the reflection of point B across line G. Point K is the reflection of point M across line Z. Point L is the reflection of point M across... | 9.58 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center N and circumradius 8. Let S be the line through points G and I. Line Q passes through point L parallel to line S. Segment NB and line Q intersect at point M. Find the distance between points M and L. Express your answer as a decimal number rounde... | 6.93 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 5. Line L passes through points B and A. Point K is the reflection of point E across line L. Point M is the reflection of point K across point B. Point T is the reflection of point C across point M. Find the length of segment KT. Express y... | 25.0 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center P and circumradius 6. Let L be the perpendicular bisector of segment PB. Point R is the reflection of point A across line L. Point G is the midpoint of segment AR. What is the length of segment BG? Express your answer as a decimal number rounded to 2 decima... | 6.45 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center K and circumradius 4. Let W be the rotation of point B by angle 2pi/3 around point H. Point J is obtained by rotating point W by angle pi/6 about point A. Line S is the perpendicular bisector of segment JG. Point M is the reflection of point B across l... | 10.71 | MATH |
[
{
"content": "ABCDFG is a regular hexagon with center E and circumradius 5. Point T is the midpoint of segment AB. Point O is the reflection of point T across point C. Let S be the midpoint of segment EC. Find the length of segment OS. Express your answer as a decimal number rounded to 2 decimal places.\n\nPres... | 8.66 | MATH |
[
{
"content": "ABCDEGHIJK is a regular 10-gon with center F and circumradius 5. Let S be the line through point D perpendicular to segment GB. Line O is the reflection of line S across point G. Let Y be the angle bisector of angle AEI. Line N is the reflection of line Y across line O. Point L is the reflection o... | 31.93 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Z and circumradius 10. Line R is the angle bisector of angle HFD. Let L be the line through point A parallel to line R. Line X is the reflection of line L across line R. Let T be the midpoint of segment ZD. Point Y is the reflection of point T across line ... | 13.55 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center L and circumradius 12. Line X is the perpendicular bisector of segment BI. Line J passes through point B parallel to line X. Let S be the reflection of line J through point D. Point V is the reflection of point C across line S. Let R be the reflection of po... | 33.87 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center I and circumradius 6. Let O be the perpendicular bisector of segment FE. Line P passes through point B parallel to line O. Let Y be the line through point E parallel to line P. Point V is the reflection of point F across line Y. Find the length of segment AV... | 15.87 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center P and circumradius 6. Let M be the midpoint of segment CF. Let N be the midpoint of segment FM. Let T be the midpoint of segment BP. Find the distance between points N and T. Express your answer as a decimal number rounded to 2 decimal places.\n\nPres... | 6.47 | MATH |
[
{
"content": "ABCDEFHIJKLM is a regular dodecagon with center G and circumradius 9. Point R is the reflection of point C across point D. Let X be the line through points K and R. Line Z passes through point L parallel to segment FG. Point V is the intersection of lines X and Z. Find the distance between points ... | 8.83 | MATH |
[
{
"content": "Let ACDEFGHI be a regular octagon with center B and circumradius 2. Line W is the angle bisector of angle HEA. Let O be the midpoint of segment CI. Line Q is the reflection of line W across point A. Point P is the reflection of point G across line Q. Find the length of segment OP. Express your ans... | 6.73 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center W and circumradius 8. Let L be the line through points W and C. Let K be the line through point F parallel to line L. Let M be the reflection of line K through point D. Point R is the reflection of point H across line M. Find the length of segment RW. Exp... | 8.77 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center G and circumradius 5. Let Y be the line through points A and E. Let L be the perpendicular bisector of segment ED. Let M be the perpendicular bisector of segment EC. Let V be the rotation of point B by angle pi/3 around point E. Line O is the reflection of line... | 32.85 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 4. Let L be the line through point G perpendicular to segment DE. Point K is the reflection of point A across line L. Point S is the midpoint of segment FK. What is the length of segment SB? Express your answer as a decimal number ro... | 10.01 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center H and circumradius 7. Let Q be the line through points C and B. Line R is the angle bisector of angle FBA. Line L is the reflection of line Q across line R. Point Z is the reflection of point E across line L. Find the length of segment DZ. Express your a... | 7.0 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center J and circumradius 1. Let N be the circumcircle of polygon ABCDE. Let V be the reflection of point J across point C. Let K be the inversion of point V in circle N. Let H be the midpoint of segment JK. What is the measure of angle DCH, in radians? Express your a... | 0.94 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Q and circumradius 3. Let Y be the angle bisector of angle FEA. Let Z be the reflection of line Y through point B. Point X is the reflection of point L across line Z. Point T is the midpoint of segment XA. What is the length of segment TD? Express yo... | 7.76 | MATH |
[
{
"content": "ABCEF is a regular 5-gon with center D and circumradius 4. Let W be the perpendicular bisector of segment BF. Line S passes through point D perpendicular to line W. Line R is the reflection of line W across point C. Let M be the line through point F perpendicular to line R. Let I be the reflection... | 6.47 | MATH |
[
{
"content": "Let BCDEF be a regular 5-gon with center A and circumradius 1. Point T is the midpoint of segment FD. Let P be the reflection of point F across point C. Let S be the angle bisector of angle PAB. Point U is the reflection of point F across line S. Point V is the reflection of point U across point T... | 0.88 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 1. Let J be the line through point H perpendicular to segment AE. Let Y be the reflection of line J through point D. Point T is the reflection of point H across line Y. What is the length of segment IT? Express your answer as a decim... | 3.55 | MATH |
[
{
"content": "Let ACDEFGHIJ be a regular 9-gon with center B and circumradius 11. Let L be the midpoint of segment IG. Point X is the reflection of point A across segment IG. Point K is the reflection of point L across segment HX. What is the distance between points K and I? Express your answer as a decimal num... | 9.84 | MATH |
[
{
"content": "Let ABCEFG be a regular hexagon with center D and circumradius 6. Point R is the midpoint of segment CE. Let U be the circumcircle of polygon ABCEFG. Line J passes through points A and B. Let Z be the inversion of point R in circle U. Line K is the reflection of line J across point Z. Point M is t... | 27.5 | MATH |
[
{
"content": "ABCDEFGIJK is a regular 10-gon with center H and circumradius 5. Point V is the midpoint of segment JE. Let W be the midpoint of segment FK. Point O is the midpoint of segment IW. What is the distance between points V and O? Express your answer as a decimal number rounded to 2 decimal places.\n\nP... | 2.22 | MATH |
[
{
"content": "ABCDEFGHJKL is a regular 11-gon with center I and circumradius 8. Let Z be the perpendicular bisector of segment IE. Let S be the reflection of point J across point H. Point Y is the reflection of point C across segment BA. Let U be the circumcircle of polygon ABCDEFGHJKL. Let T be the reflection ... | 17.36 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 5. Let O be the midpoint of segment JG. Let P be the line through point O perpendicular to segment KH. Point T is the reflection of point D across line P. Find the length of segment TD. Express your answer as a decimal number r... | 0.67 | MATH |
[
{
"content": "Let ACDE be a square with center B and circumradius 10. Let W be the reflection of point E across point A. Let G be the rotation of point W by angle 5pi/6 around point D. Let N be the reflection of point B across point C. Let J be the midpoint of segment NE. Let H be the reflection of point D acro... | 8.99 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center X and circumradius 7. Point K is the reflection of point J across point H. Point U is obtained by rotating point E by angle 5pi/6 about point I. Let T be the reflection of point B across point D. Point M is the midpoint of segment ET. Let Z be the lin... | 26.5 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center R and circumradius 6. Point Y is the reflection of point R across point D. Let V be the line through points E and A. Let P be the line through points D and C. Point X is the intersection of lines P and V. Point U is the midpoint of segment YX. What is the dista... | 4.63 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center Z and circumradius 6. Point K is the midpoint of segment AC. Point P is the midpoint of segment ZC. Let X be the circumcircle of polygon ABCDE. Let N be the inversion of point P in circle X. Find the measure of angle NZK, in radians. Express your answer as a de... | 1.26 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center J and circumradius 6. Let K be the rotation of point C by angle 5pi/12 around point J. Let P be the reflection of point D across point B. Let Q be the midpoint of segment CK. Let G be the midpoint of segment PK. Find the distance between points G and Q. ... | 7.94 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center Q and circumradius 7. Point J is the reflection of point Q across point B. Let W be the midpoint of segment JF. Segments EH and FD intersect at point O. What is the distance between points O and W? Express your answer as a decimal number rounded to 2 de... | 7.8 | MATH |
[
{
"content": "BCDE is a square with center A and circumradius 2. Point J is obtained by rotating point E by angle pi/12 about point B. Let L be the line through point J perpendicular to segment CB. Point T is the reflection of point D across line L. Point U is the reflection of point T across point E. Let I be ... | 4.52 | MATH |
[
{
"content": "Let ACDEF be a regular 5-gon with center B and circumradius 12. Point O is the midpoint of segment AF. Let W be the midpoint of segment AE. Let X be the reflection of point W across point B. Point L is the reflection of point X across point D. Let I be the midpoint of segment WO. Find the length o... | 27.38 | MATH |
[
{
"content": "Let ABDEFGH be a regular 7-gon with center C and circumradius 12. Let I be the reflection of point B across point C. Let Q be the midpoint of segment IA. Let S be the line through points A and H. Point M is the reflection of point Q across line S. Find the distance between points M and A. Express ... | 10.81 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center V and circumradius 8. Let W be the midpoint of segment FH. Let L be the circumcircle of polygon ABCDEFGH. Circle X is the reflection of circle L across point W. Let P be the inversion of point E in circle X. Find the distance between points D and P. Ex... | 13.53 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center P and circumradius 11. Let U be the rotation of point P by angle pi around point F. Line T is the angle bisector of angle DBU. Let S be the line through points A and C. Let X be the reflection of line S through point U. Let V be the line through point D ... | 33.86 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center K and circumradius 11. Let T be the angle bisector of angle CAF. Point P is on line T. Let N be the line through points C and P. Point U is the reflection of point B across line N. Find the distance between points C and U. Express your answer as a deci... | 8.42 | MATH |
[
{
"content": "ABCDEFHIJKLM is a regular dodecagon with center G and circumradius 6. Let Z be the midpoint of segment FJ. Line P is the angle bisector of angle KZE. Let V be the line through point D parallel to line P. Line R passes through point B perpendicular to line V. Point U is the reflection of point L ac... | 11.59 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center W and circumradius 12. Line Q passes through points D and B. Line T is the reflection of line Q across point A. Let O be the line through points C and E. Point U is the intersection of lines O and T. Line H passes through point A perpendicular to line Q. Point ... | 2.2 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 10. Line W passes through points C and F. Point R lies on line W. Let U be the angle bisector of angle ESR. Point Z is the reflection of point L across line U. What is the distance between points Z and S? Express your answer as a d... | 10.0 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center O and circumradius 7. Point M is the reflection of point A across segment HF. Let Q be the reflection of point A across point I. Let Z be the reflection of point M across point H. What is the distance between points Z and Q? Express your answer as a dec... | 10.58 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center T and circumradius 11. Let W be the rotation of point E by angle pi/12 around point D. Line V is the perpendicular bisector of segment BW. Let Z be the angle bisector of angle CAT. Let X be the circumcircle of polygon ABCDEF. Point G is the reflection of... | 11.8 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 7. Line O passes through points L and K. Point Q is obtained by rotating point F by angle pi/4 about point K. Point T is the midpoint of segment AQ. Line P passes through point T perpendicular to line O. Let X be the reflection... | 30.39 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.