messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "SM = 11. Point V is the reflection of point M across point S. Let E be the rotation of point V by angle pi/2 around point S. Let I be the rotation of point E by angle pi/4 around point S. Let J be the reflection of point I across point V. Let W be the vector from point M to point V. Let X be the p... | 101.37 | MATH |
[
{
"content": "Let UP = 2. Let M be the midpoint of segment UP. Let B be the rotation of point M by angle 2pi/3 around point U. Point Y is the midpoint of segment MB. Point Q is the reflection of point B across point M. Point X is the reflection of point U across segment YM. Find the distance between points Q an... | 2.65 | MATH |
[
{
"content": "Let AY = 2. Let W be the reflection of point Y across point A. Let M be the vector from point A to point W. Point O is obtained by rotating point A by angle 5pi/6 about point Y. Let K be the rotation of point A by angle 5pi/6 around point O. Let N be the reflection of point K across point A. Let R... | 3.07 | MATH |
[
{
"content": "Let MB = 5. Let U be the rotation of point B by angle pi/12 around point M. Line T passes through points B and M. Let G be the angle bisector of angle BMU. Point I is the midpoint of segment MU. Line X passes through point B parallel to line G. Line H passes through point I parallel to line T. Poi... | 4.97 | MATH |
[
{
"content": "Let RU = 10. Let V be the rotation of point R by angle pi/3 around point U. Let M be the midpoint of segment UR. Let N be the rotation of point R by angle 11pi/12 around point V. Point C is the reflection of point V across point R. Point Y is the reflection of point U across point N. Let T be the ... | 23.59 | MATH |
[
{
"content": "Let PX = 9. Let W be the reflection of point P across point X. Let A be the perpendicular bisector of segment PW. Let K be the reflection of line A through point W. Point L is the reflection of point X across line K. Let F be the perpendicular bisector of segment XW. Let Y be the rotation of point... | 4.5 | MATH |
[
{
"content": "Let NV = 9. Let O be the reflection of point N across point V. Let H be the perpendicular bisector of segment VO. Point S is the midpoint of segment NV. Line U is the reflection of line H across point S. Point C is the reflection of point O across line U. Find the length of segment OC. Express you... | 45.0 | MATH |
[
{
"content": "UC = 1. Point F is obtained by rotating point U by angle 11pi/12 about point C. Point Q is the reflection of point C across point F. Let V be the rotation of point F by angle pi/4 around point C. Point B is the reflection of point U across point V. Let Z be the line through points U and C. Point P... | 1.55 | MATH |
[
{
"content": "Let DS = 10. Point P is the midpoint of segment DS. Let X be the rotation of point S by angle 7pi/12 around point P. Point Z is the reflection of point X across point D. Point L is the reflection of point D across point Z. Point B is the midpoint of segment PZ. Line F is the angle bisector of angl... | 0.77 | MATH |
[
{
"content": "Let VG = 5. Line P is the perpendicular bisector of segment GV. Line X passes through point G perpendicular to segment VG. Let Y be the reflection of line P across line X. Let D be the reflection of line X across line Y. Point A is on line X. Point Q is the reflection of point A across line D. Wha... | 10.0 | MATH |
[
{
"content": "Let KX = 7. Let F be the reflection of point X across point K. Point S is the midpoint of segment FK. Let O be the vector from point F to point K. Line A is the angle bisector of angle FSK. Let E be the perpendicular bisector of segment SX. Point C is on line E. Point M is the reflection of point ... | 3.5 | MATH |
[
{
"content": "JL = 11. Let Y be the midpoint of segment JL. Point N is obtained by rotating point J by angle pi/6 about point L. Line W passes through points N and L. Point S is obtained by rotating point Y by angle pi/6 about point J. Let Z be the line through point S parallel to segment JL. Line C is the refl... | 11.51 | MATH |
[
{
"content": "UF = 10. Let K be the rotation of point F by angle 3pi/4 around point U. Let N be the line through point K perpendicular to segment UK. Line I passes through point F perpendicular to line N. Point R is the reflection of point K across line I. Line A is the reflection of line I across point K. Poin... | 27.1 | MATH |
[
{
"content": "KM = 2. Let Z be the rotation of point K by angle pi/6 around point M. Line N passes through points K and Z. Let Y be the line through point Z perpendicular to segment MK. Let Q be the reflection of line Y across line N. Point T is the reflection of point M across line Q. Point R is the reflection... | 1.0 | MATH |
[
{
"content": "Let QM = 6. Let X be the perpendicular bisector of segment QM. Let G be the reflection of line X through point M. Point F lies on line G at distance 6 from point Q. Point L is the midpoint of segment FQ. Let U be the perpendicular bisector of segment LQ. Point C is the reflection of point F across... | 4.56 | MATH |
[
{
"content": "Let PV = 8. Point C is the midpoint of segment VP. Let L be the angle bisector of angle VCP. Let Z be the perpendicular bisector of segment CP. Let W be the reflection of point V across point P. Line A is the reflection of line Z across point P. Let H be the reflection of line L through point P. P... | 2.0 | MATH |
[
{
"content": "Let IE = 5. A is constructed so that EA = 5. Let O be the reflection of point A across point E. Point L is obtained by rotating point A by angle pi/6 about point O. Let J be the vector from point A to point O. Let Z be the rotation of point O by angle pi/4 around point A. Point R is the translatio... | 7.15 | MATH |
[
{
"content": "Let MX = 6. Line R is the perpendicular bisector of segment XM. Let F be the rotation of point X by angle 5pi/6 around point M. Line V passes through points X and F. Let I be the midpoint of segment FX. Point S is obtained by rotating point I by angle 5pi/6 about point X. Let D be the reflection o... | 33.86 | MATH |
[
{
"content": "Let IF = 3. Point O is the midpoint of segment IF. Point V is obtained by rotating point I by angle 11pi/12 about point O. Let B be the perpendicular bisector of segment FO. Let K be the rotation of point V by angle 11pi/12 around point O. Line A is the perpendicular bisector of segment FI. Line U... | 1.5 | MATH |
[
{
"content": "Let BJ = 6. Point L is the reflection of point J across point B. Let Z be the vector from point B to point J. Point W is obtained by rotating point L by angle 5pi/12 about point B. Let Q be the rotation of point W by angle pi/2 around point L. Point O is the translation of point Q by vector Z. Poi... | 15.98 | MATH |
[
{
"content": "XS = 1. Line C passes through points S and X. Let O be the line through point X perpendicular to line C. Let U be the rotation of point X by angle pi/3 around point S. Point F is the reflection of point S across line O. Let E be the reflection of point S across point U. Point M is the reflection o... | 2.0 | MATH |
[
{
"content": "RL = 4. Point C is the midpoint of segment RL. Let W be the vector from point R to point L. Point M is obtained by rotating point L by angle 3pi/4 about point R. Let X be the angle bisector of angle MRC. Point T is the midpoint of segment LC. Line P passes through point T perpendicular to line X. ... | 10.34 | MATH |
[
{
"content": "Let BC = 8. Point U is obtained by rotating point C by angle 11pi/12 about point B. Line G is the angle bisector of angle BCU. Point P is the reflection of point U across line G. Let F be the line through point P parallel to line G. Line Z passes through point U parallel to line F. Point W is the ... | 8.65 | MATH |
[
{
"content": "Let WR = 4. Point X is obtained by rotating point W by angle pi/4 about point R. Point N is obtained by rotating point R by angle pi/12 about point X. Line B passes through points N and X. Let J be the midpoint of segment NW. Point Z is the reflection of point J across line B. Let T be the reflect... | 6.29 | MATH |
[
{
"content": "LP = 11. Let O be the midpoint of segment LP. Line R is the perpendicular bisector of segment PL. Point G is obtained by rotating point L by angle 11pi/12 about point O. Let F be the line through point G perpendicular to line R. Line T is the perpendicular bisector of segment GL. Let V be the refl... | 6.19 | MATH |
[
{
"content": "UJ = 4. Let V be the vector from point J to point U. Let A be the reflection of point J across point U. Point N is obtained by rotating point U by angle 5pi/12 about point J. Let B be the rotation of point N by angle 7pi/12 around point U. Let X be point A translated by vector V. Let W be the rota... | 1.31 | MATH |
[
{
"content": "AT = 2. Let C be the reflection of point A across point T. Point F is the reflection of point T across point A. Line H is the perpendicular bisector of segment TC. Let P be the rotation of point A by angle 7pi/12 around point T. Point W is the reflection of point A across point F. Let Q be the per... | 7.73 | MATH |
[
{
"content": "RE = 12. Point H is obtained by rotating point R by angle 5pi/6 about point E. Point M is obtained by rotating point E by angle pi/12 about point H. Point W is the reflection of point E across point M. Point G is the reflection of point H across segment MW. Point O is the reflection of point G acr... | 25.58 | MATH |
[
{
"content": "JW = 3. Line H passes through point J perpendicular to segment JW. Point U is on line H with |UJ| = 7. Point D is the reflection of point J across point U. Line B passes through point U perpendicular to line H. Point P is the reflection of point W across line B. Line E is the perpendicular bisecto... | 6.39 | MATH |
[
{
"content": "XP = 10. Point E is obtained by rotating point X by angle 5pi/12 about point P. Point T is the reflection of point X across point E. Let B be the perpendicular bisector of segment XT. Let V be the line through point T parallel to line B. Let G be the rotation of point P by angle 7pi/12 around poin... | 31.51 | MATH |
[
{
"content": "CD = 8. Point I is the midpoint of segment CD. Let S be the perpendicular bisector of segment ID. Point E is the reflection of point C across line S. Line N passes through point E parallel to line S. Let V be the line through point I parallel to line N. Line H passes through points E and C. Line U... | 11.49 | MATH |
[
{
"content": "DH = 12. Point N is obtained by rotating point H by angle pi/2 about point D. Point V is obtained by rotating point N by angle 7pi/12 about point H. Point K is the reflection of point D across point H. Point B is obtained by rotating point N by angle pi/2 about point H. Let T be the angle bisector... | 65.99 | MATH |
[
{
"content": "WK = 6. Let A be the reflection of point W across point K. Let D be the midpoint of segment WK. Point X is obtained by rotating point A by angle 7pi/12 about point W. Point I is the midpoint of segment KX. Let R be the midpoint of segment KD. Let F be the reflection of point X across point A. Poin... | 25.4 | MATH |
[
{
"content": "Let FX = 10. Line E is the perpendicular bisector of segment FX. Let W be the midpoint of segment FX. Point Z is on line E with |ZX| = 12. Line A passes through point Z perpendicular to line E. Point D lies on segment FX. Line J is the reflection of line A across point D. Point Y is the reflection... | 24.52 | MATH |
[
{
"content": "RL = 2. Let W be the midpoint of segment LR. Let S be the rotation of point L by angle pi/2 around point W. Let F be the midpoint of segment LS. Point O is the midpoint of segment FL. Let X be the midpoint of segment WL. Point N is the midpoint of segment XO. Find the length of segment NS. Express... | 1.08 | MATH |
[
{
"content": "Let CS = 9. Point I is obtained by rotating point C by angle 11pi/12 about point S. Line G is the angle bisector of angle ISC. Point K is the midpoint of segment SC. Line Z is the angle bisector of angle IKC. Let E be the rotation of point I by angle 7pi/12 around point K. Let P be the perpendicul... | 15.72 | MATH |
[
{
"content": "Let VY = 4. Point T is the reflection of point V across point Y. Let K be the rotation of point Y by angle 11pi/12 around point T. Let C be the line through points V and K. Point L is the reflection of point K across point Y. Let E be the perpendicular bisector of segment LY. Point I is the midpoi... | 15.87 | MATH |
[
{
"content": "Let ZK = 4. Let I be the rotation of point K by angle 5pi/12 around point Z. Let M be the perpendicular bisector of segment KI. Let D be the line through point K parallel to line M. Point F is the reflection of point I across line D. Point L is the midpoint of segment FZ. Let O be the midpoint of ... | 13.62 | MATH |
[
{
"content": "Let JL = 10. Let G be the rotation of point L by angle pi/3 around point J. Point Y is the reflection of point G across point J. Point U is obtained by rotating point G by angle pi/3 about point Y. Point K is obtained by rotating point Y by angle pi/2 about point J. Point I is the midpoint of segm... | 2.36 | MATH |
[
{
"content": "QS = 10. Let Y be the rotation of point Q by angle pi/3 around point S. Let T be the midpoint of segment SY. Let M be the midpoint of segment YQ. Let U be the midpoint of segment TQ. Point O is the reflection of point S across segment UY. Find the distance between points M and O. Express your answ... | 5.67 | MATH |
[
{
"content": "LF = 9. Point E is the reflection of point F across point L. Let J be the midpoint of segment FL. Let Y be the midpoint of segment EJ. Line U is the angle bisector of angle LYE. Point X is the reflection of point L across line U. Point M is on line U with |ML| = 5. Point I is the reflection of poi... | 37.21 | MATH |
[
{
"content": "DH = 5. Let I be the rotation of point D by angle 2pi/3 around point H. Point U is obtained by rotating point D by angle 5pi/12 about point H. Point P is obtained by rotating point I by angle 5pi/6 about point D. Point K is obtained by rotating point I by angle pi/3 about point P. Line W passes th... | 10.24 | MATH |
[
{
"content": "Let HM = 9. Point T is the reflection of point H across point M. Point E is obtained by rotating point M by angle pi/6 about point H. Point S is the midpoint of segment HE. Point V is the reflection of point S across point T. Let C be the perpendicular bisector of segment VE. Let O be the reflecti... | 40.01 | MATH |
[
{
"content": "Let EM = 5. Let J be the rotation of point E by angle 7pi/12 around point M. Let D be the rotation of point J by angle 5pi/6 around point E. Let S be the midpoint of segment MJ. Let F be the rotation of point S by angle pi/3 around point J. Let C be the reflection of point D across point F. Let X ... | 35.34 | MATH |
[
{
"content": "TR = 2. Point C is the reflection of point R across point T. Point K is the reflection of point T across point C. Point Z is obtained by rotating point T by angle pi about point K. Let Q be the rotation of point K by angle 2pi/3 around point R. Line H is the angle bisector of angle QTZ. Let M be t... | 3.76 | MATH |
[
{
"content": "Let UG = 2. Point C is the midpoint of segment UG. Let B be the midpoint of segment CG. Let O be the midpoint of segment BG. Let J be the midpoint of segment OB. Find the distance between points O and J. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in ... | 0.12 | MATH |
[
{
"content": "Let NP = 8. Point S is the midpoint of segment PN. Let Q be the midpoint of segment SP. Let R be the reflection of point Q across point S. Let I be the angle bisector of angle PQR. Point O is obtained by rotating point S by angle 5pi/12 about point Q. Point H is the midpoint of segment RN. Point C... | 13.89 | MATH |
[
{
"content": "Let LY = 1. Point E is the midpoint of segment YL. Point J is obtained by rotating point L by angle 11pi/12 about point E. Point D is obtained by rotating point Y by angle 5pi/6 about point J. Let Q be the rotation of point L by angle pi/3 around point Y. Let X be the rotation of point Q by angle ... | 1.2 | MATH |
[
{
"content": "Let GN = 5. Point M is obtained by rotating point N by angle 7pi/12 about point G. Line H passes through point M perpendicular to segment NM. Let W be the line through point G perpendicular to line H. Point V is the reflection of point N across line W. Let U be the reflection of point G across poi... | 3.04 | MATH |
[
{
"content": "WF = 2. Point M is obtained by rotating point W by angle pi/4 about point F. Point K is obtained by rotating point W by angle 5pi/12 about point F. Point C is the reflection of point K across point W. Let D be the midpoint of segment KW. Line P is the angle bisector of angle DMF. Line N is the ref... | 0.83 | MATH |
[
{
"content": "Let DF = 8. Let G be the perpendicular bisector of segment DF. Let Z be the line through points F and D. Let R be the line through point D parallel to line G. Line I passes through point F parallel to line R. Point S lies on line I at distance 5 from point F. Let Q be the rotation of point S by an... | 28.33 | MATH |
[
{
"content": "Let IM = 5. Line L is the perpendicular bisector of segment MI. Let Z be the line through point M parallel to line L. Let A be the reflection of line L across line Z. Point E is obtained by rotating point M by angle pi/12 about point I. Let J be the reflection of point E across point I. Let H be t... | 17.48 | MATH |
[
{
"content": "LR = 3. Let N be the reflection of point R across point L. Let I be the rotation of point N by angle 5pi/12 around point L. Let B be the rotation of point R by angle 7pi/12 around point N. Point W is obtained by rotating point B by angle pi/2 about point N. Point Z is the midpoint of segment NB. P... | 3.74 | MATH |
[
{
"content": "WU = 12. Let L be the vector from point W to point U. Let Z be point U translated by vector L. Point O is obtained by rotating point Z by angle 3pi/4 about point W. Point G is obtained by rotating point Z by angle 5pi/12 about point U. Let C be the perpendicular bisector of segment ZO. Point F is ... | 80.85 | MATH |
[
{
"content": "Let PR = 10. Line X passes through points R and P. Point O lies on line X at distance 5 from point P. Point D is obtained by rotating point O by angle pi/6 about point P. Let A be the vector from point D to point P. Point I is the translation of point P by vector A. Let G be the perpendicular bise... | 41.25 | MATH |
[
{
"content": "HE = 1. Let U be the line through points H and E. Let Z be the rotation of point E by angle pi/12 around point H. Point X is the midpoint of segment ZE. Line K passes through point Z parallel to line U. Line R passes through points H and Z. Point Y is the reflection of point X across line R. Let D... | 1.42 | MATH |
[
{
"content": "MQ = 2. Let P be the perpendicular bisector of segment MQ. Let A be the midpoint of segment QM. Point G is the reflection of point A across point Q. Point Y lies on line P at distance 11 from point G. Line R passes through point Y parallel to segment MQ. Line B is the reflection of line R across p... | 27.54 | MATH |
[
{
"content": "QL = 3. Point N is obtained by rotating point L by angle 3pi/4 about point Q. Point Z is the reflection of point Q across point L. Point W is the midpoint of segment NZ. Let H be the midpoint of segment QW. What is the distance between points H and Z? Express your answer as a decimal number rounde... | 5.06 | MATH |
[
{
"content": "JT = 3. Line Q passes through points T and J. Let F be the rotation of point T by angle pi/12 around point J. Point V is obtained by rotating point J by angle pi/3 about point F. Line O is the perpendicular bisector of segment FV. Line N passes through point F parallel to line O. Let L be the refl... | 9.28 | MATH |
[
{
"content": "Let AF = 12. Line E passes through points A and F. Let K be the rotation of point F by angle pi/6 around point A. Point O is obtained by rotating point A by angle 3pi/4 about point F. Let R be the reflection of point K across point O. Let B be the reflection of point R across point A. Point I is t... | 37.07 | MATH |
[
{
"content": "FJ = 10. Point A is the midpoint of segment JF. Let B be the rotation of point A by angle pi/12 around point F. Line I is the perpendicular bisector of segment AF. Line V passes through point B perpendicular to line I. Let T be the line through points J and B. Point K lies on segment JF. Point M i... | 2.59 | MATH |
[
{
"content": "IV = 6. Let Z be the midpoint of segment IV. Let L be the midpoint of segment ZI. Point A is obtained by rotating point I by angle pi/12 about point L. Let J be the reflection of point V across point L. Let G be the midpoint of segment AJ. Point R is the reflection of point G across point J. What ... | 7.53 | MATH |
[
{
"content": "Let KC = 10. Point V is obtained by rotating point C by angle 5pi/6 about point K. Let T be the rotation of point V by angle 3pi/4 around point K. Point E is the midpoint of segment TK. Let Q be the line through points E and V. Line B is the angle bisector of angle TVC. Let L be the line through p... | 34.76 | MATH |
[
{
"content": "Let ET = 9. Let Q be the midpoint of segment ET. Let F be the perpendicular bisector of segment TQ. Line W passes through point T parallel to line F. Point X is the midpoint of segment QE. Point H is the reflection of point E across line W. Let M be the rotation of point E by angle 5pi/12 around p... | 10.36 | MATH |
[
{
"content": "Let XT = 4. Point E is obtained by rotating point T by angle pi/4 about point X. Point M is the reflection of point X across point E. Let W be the reflection of point E across point X. Point Q is the reflection of point W across segment TE. Point F is the midpoint of segment TE. Let R be the refle... | 12.66 | MATH |
[
{
"content": "Let UE = 5. Point Z is obtained by rotating point U by angle pi/6 about point E. Point K is the reflection of point U across point Z. Line D is the angle bisector of angle EZU. Point O is obtained by rotating point U by angle 11pi/12 about point K. Let S be the midpoint of segment EK. Line P is th... | 19.64 | MATH |
[
{
"content": "QX = 1. Let N be the reflection of point X across point Q. Let M be the perpendicular bisector of segment XQ. Point Z is the reflection of point N across line M. Let A be the line through points X and Z. Let V be the line through point Q perpendicular to line A. Point J is the reflection of point ... | 1.0 | MATH |
[
{
"content": "Let HX = 9. Let Q be the vector from point H to point X. Let J be the perpendicular bisector of segment XH. Let O be the rotation of point X by angle pi around point H. Let E be point X translated by vector Q. Point U lies on line J at distance 8 from point E. Line Z passes through points U and E.... | 24.21 | MATH |
[
{
"content": "Let YL = 9. Let X be the vector from point Y to point L. Let B be the midpoint of segment LY. Let E be point B translated by vector X. Let C be the rotation of point E by angle 3pi/4 around point L. Let J be point C translated by vector X. Point N is the reflection of point C across point B. Let M... | 12.54 | MATH |
[
{
"content": "Let SF = 6. Point C is the midpoint of segment FS. Let B be the perpendicular bisector of segment FS. Let G be the line through point F parallel to line B. Let P be the rotation of point F by angle 5pi/12 around point S. Let T be the midpoint of segment PS. Let E be the rotation of point S by angl... | 16.81 | MATH |
[
{
"content": "Let ZG = 1. Point Y is obtained by rotating point G by angle 11pi/12 about point Z. Line I is the angle bisector of angle ZGY. Let B be the perpendicular bisector of segment ZY. Point D is the midpoint of segment ZY. Line C is the reflection of line I across line B. Let V be the midpoint of segmen... | 0.88 | MATH |
[
{
"content": "RX = 2. Point K is obtained by rotating point X by angle pi/3 about point R. Line O is the perpendicular bisector of segment XK. Let J be the line through points R and X. Line B passes through point R perpendicular to line O. Point A is the reflection of point K across line B. Let Z be the reflect... | 0.86 | MATH |
[
{
"content": "Let KJ = 6. Point H is the reflection of point K across point J. Let R be the rotation of point H by angle 2pi/3 around point K. Point S is the reflection of point K across point R. Let P be the vector from point S to point R. Point B is the translation of point H by vector P. Let I be the rotatio... | 54.26 | MATH |
[
{
"content": "XT = 2. Let D be the rotation of point X by angle 7pi/12 around point T. Let C be the midpoint of segment TX. Point Z is the midpoint of segment CD. Point P is the reflection of point Z across segment CT. Point M is the midpoint of segment CT. Point A is the reflection of point P across point Z. P... | 3.16 | MATH |
[
{
"content": "HW = 11. Point K is obtained by rotating point H by angle pi/12 about point W. Let P be the midpoint of segment HK. Let A be the angle bisector of angle PWK. Point C is the reflection of point P across line A. Point Z is the reflection of point C across point P. What is the length of segment CZ? E... | 2.85 | MATH |
[
{
"content": "Let BZ = 4. Let G be the vector from point Z to point B. Let J be the reflection of point Z across point B. Line S is the angle bisector of angle JBZ. Point Q is the translation of point J by vector G. Line E is the reflection of line S across point Q. Line F is the reflection of line E across lin... | 31.0 | MATH |
[
{
"content": "OW = 6. Line N passes through point O perpendicular to segment WO. Let M be the perpendicular bisector of segment OW. Let S be the line through point W parallel to line N. Let T be the midpoint of segment WO. Point V is the reflection of point T across line S. Let Y be the rotation of point O by a... | 20.63 | MATH |
[
{
"content": "IF = 1. Let X be the rotation of point I by angle 5pi/6 around point F. Let Z be the reflection of point I across point X. Let Y be the midpoint of segment FX. Line H is the perpendicular bisector of segment ZY. Point E is the reflection of point F across line H. Point M is the midpoint of segment... | 1.45 | MATH |
[
{
"content": "Let FI = 10. Let J be the midpoint of segment FI. Let S be the vector from point I to point F. Point Z is the midpoint of segment IJ. Line L passes through point Z perpendicular to segment JF. Line G passes through point J parallel to line L. Let K be the reflection of line L through point F. Poin... | 64.87 | MATH |
[
{
"content": "AB = 7. Let F be the reflection of point A across point B. Let K be the midpoint of segment BA. Line J passes through point F perpendicular to segment BA. Let P be the reflection of line J through point A. Point G is the reflection of point K across line P. Line I passes through point G parallel t... | 81.63 | MATH |
[
{
"content": "VF = 11. Let H be the midpoint of segment VF. Line U is the angle bisector of angle FHV. Point Z lies on line U at distance 8 from point H. Let C be the line through points H and F. Line B is the perpendicular bisector of segment FZ. Line G is the perpendicular bisector of segment HF. Point T is t... | 14.79 | MATH |
[
{
"content": "Let YS = 11. Point U is the midpoint of segment YS. Point O is obtained by rotating point Y by angle pi/4 about point U. Let Z be the rotation of point S by angle 2pi/3 around point O. Point W is the reflection of point Y across point O. Point N is the reflection of point U across point W. Point C... | 5.84 | MATH |
[
{
"content": "QS = 12. Point I is obtained by rotating point Q by angle pi/12 about point S. Let L be the vector from point S to point I. Point T is the translation of point I by vector L. Point E lies on segment SQ. Point N is obtained by rotating point I by angle 3pi/4 about point Q. Let C be the midpoint of ... | 11.07 | MATH |
[
{
"content": "AF = 1. Point N is the midpoint of segment FA. Point V is obtained by rotating point A by angle pi about point F. Let S be the angle bisector of angle FNA. Let D be the line through point F parallel to line S. Point C is the midpoint of segment VF. Let Y be the rotation of point A by angle 2pi/3 a... | 2.09 | MATH |
[
{
"content": "Let BG = 5. Point K is obtained by rotating point B by angle pi/4 about point G. Point X is the midpoint of segment KG. Line R passes through point G perpendicular to segment BG. Point N is the reflection of point K across line R. Let L be the reflection of point X across point N. Find the length ... | 11.18 | MATH |
[
{
"content": "BC = 1. Let Q be the midpoint of segment CB. Line E passes through point C perpendicular to segment CB. Point P is on line E with |PC| = 10. Point M is the midpoint of segment QB. Point D is the reflection of point P across point M. Let I be the line through point D parallel to line E. Point J is ... | 1.25 | MATH |
[
{
"content": "Let WI = 8. Point X is obtained by rotating point W by angle 11pi/12 about point I. Line H passes through points W and X. Line S is the perpendicular bisector of segment IX. Point N is the reflection of point I across line H. Let B be the vector from point N to point I. Point E is the reflection o... | 12.83 | MATH |
[
{
"content": "GL = 9. Line F passes through points G and L. Point J lies on line F at distance 10 from point G. Let S be the midpoint of segment JG. Line M passes through point S perpendicular to line F. Line O is the perpendicular bisector of segment SL. Point W lies on line O at distance 11 from point L. Poin... | 17.0 | MATH |
[
{
"content": "Let TQ = 6. Point S is the reflection of point Q across point T. Let V be the rotation of point S by angle pi around point Q. Let E be the rotation of point V by angle 11pi/12 around point Q. Point P is obtained by rotating point Q by angle 5pi/12 about point E. Let Y be the midpoint of segment VT... | 21.98 | MATH |
[
{
"content": "Let YU = 12. Let P be the reflection of point Y across point U. Let S be the midpoint of segment UY. Let W be the reflection of point U across point Y. Line X is the angle bisector of angle PUS. Let K be the angle bisector of angle UYW. Point A is the reflection of point S across line K. Point H i... | 24.0 | MATH |
[
{
"content": "FW = 1. Point V is obtained by rotating point W by angle 3pi/4 about point F. Point I is the reflection of point V across segment WF. Let X be the line through points I and W. Point J is the reflection of point V across line X. Let S be the reflection of point V across point W. Point M is the refl... | 13.07 | MATH |
[
{
"content": "Let FU = 2. Line S is the perpendicular bisector of segment UF. Let C be the midpoint of segment UF. Let L be the reflection of point C across point F. Point M is obtained by rotating point F by angle 11pi/12 about point C. Let G be the line through point F parallel to line S. Let X be the reflect... | 2.01 | MATH |
[
{
"content": "Let YL = 5. Let J be the line through point Y perpendicular to segment LY. Point U lies on line J at distance 3 from point L. Let S be the angle bisector of angle LYU. Line N is the reflection of line S across point U. Point V is the reflection of point U across line N. Point I is the reflection o... | 12.0 | MATH |
[
{
"content": "Let KB = 3. Let W be the reflection of point K across point B. Point F is obtained by rotating point K by angle 2pi/3 about point W. Let D be the perpendicular bisector of segment FW. Let V be the reflection of line D through point F. Point S is the reflection of point K across line V. Let I be th... | 10.82 | MATH |
[
{
"content": "CJ = 3. Let T be the rotation of point J by angle 7pi/12 around point C. Let P be the reflection of point T across point C. Let K be the vector from point P to point C. Point M is the translation of point J by vector K. Point I is obtained by rotating point C by angle 3pi/4 about point P. Point X ... | 1.84 | MATH |
[
{
"content": "Let VY = 11. Let P be the line through points V and Y. Point D is obtained by rotating point Y by angle 5pi/12 about point V. Let M be the reflection of point D across point V. Line G is the perpendicular bisector of segment VD. Line E passes through point V parallel to line G. Let Q be the line t... | 0.76 | MATH |
[
{
"content": "QH = 3. Let P be the rotation of point H by angle 11pi/12 around point Q. Let B be the perpendicular bisector of segment QP. Point T is the midpoint of segment PQ. Let U be the line through points T and H. Point K is the reflection of point Q across point P. Let C be the reflection of line B throu... | 6.24 | MATH |
[
{
"content": "QN = 2. Point B is the reflection of point N across point Q. Let A be the line through points B and Q. Let Z be the vector from point B to point Q. Point J is the midpoint of segment BQ. Let L be point J translated by vector Z. Let D be the rotation of point Q by angle 11pi/12 around point J. Let ... | 1.24 | MATH |
[
{
"content": "RT = 3. Let H be the reflection of point T across point R. Let G be the midpoint of segment RT. Let L be the rotation of point T by angle pi/3 around point R. Let Z be the midpoint of segment HR. Let A be the rotation of point H by angle pi/3 around point T. Let M be the rotation of point T by ang... | 1.33 | MATH |
[
{
"content": "HX = 2. Let O be the reflection of point X across point H. Let N be the angle bisector of angle XHO. Let G be the perpendicular bisector of segment HO. Point Z lies on line N at distance 9 from point O. Point B is the midpoint of segment HX. Let L be the reflection of line N across line G. Point U... | 20.01 | MATH |
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