messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
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[
{
"content": "Let SV = 2. Let G be the reflection of point S across point V. Point W is the midpoint of segment GV. Let N be the perpendicular bisector of segment SG. Point R is the reflection of point W across line N. Find the distance between points G and R. Express your answer as a decimal number rounded to ... | 3.0 | MATH |
[
{
"content": "Let TG = 7. Point X is the midpoint of segment GT. Let N be the rotation of point G by angle pi/12 around point X. Point M is the reflection of point N across point X. Let O be the line through points N and X. Line V passes through point T perpendicular to line O. Let K be the reflection of point ... | 0.97 | MATH |
[
{
"content": "Let JN = 4. Point W is obtained by rotating point N by angle pi/2 about point J. Point C is the reflection of point N across point W. Let O be the midpoint of segment JN. Point R is the midpoint of segment OC. Let Z be the perpendicular bisector of segment RN. Let M be the line through point W par... | 7.89 | MATH |
[
{
"content": "Let FT = 11. Let U be the perpendicular bisector of segment TF. Let G be the rotation of point F by angle 5pi/12 around point T. Let M be the midpoint of segment GF. Let L be the reflection of line U through point T. Point J is the reflection of point G across line U. Let P be the midpoint of segm... | 59.01 | MATH |
[
{
"content": "SK = 5. Let L be the perpendicular bisector of segment SK. Point J is on line L with |JK| = 9. Point P is the reflection of point J across segment SK. Point F is the midpoint of segment SK. Let E be the reflection of point P across point J. Let T be the midpoint of segment FK. Let I be the line th... | 13.94 | MATH |
[
{
"content": "Let WL = 2. Point U is obtained by rotating point W by angle 3pi/4 about point L. Point E is obtained by rotating point U by angle pi/12 about point L. Point I is the midpoint of segment WL. Point Q is the midpoint of segment LE. Line F passes through point L perpendicular to segment WL. Point R i... | 0.52 | MATH |
[
{
"content": "IW = 3. Let K be the rotation of point W by angle pi/4 around point I. Point C is obtained by rotating point K by angle 5pi/12 about point W. Point B is the reflection of point W across segment IK. Point J is the midpoint of segment KC. Let O be the reflection of point B across point C. Let S be t... | 9.02 | MATH |
[
{
"content": "FD = 12. Let H be the midpoint of segment FD. Point P is the midpoint of segment FH. Let I be the rotation of point D by angle 2pi/3 around point P. Let L be the line through point I parallel to segment DF. Point Z is the midpoint of segment IH. Point J is the reflection of point Z across line L. ... | 25.48 | MATH |
[
{
"content": "FA = 9. Let H be the rotation of point F by angle 5pi/12 around point A. Point Y is the midpoint of segment AH. Point D is the midpoint of segment AY. Let N be the reflection of point F across point D. Point I is the midpoint of segment AN. Point K is the reflection of point I across segment ND. W... | 4.48 | MATH |
[
{
"content": "HW = 3. Point S is obtained by rotating point H by angle 2pi/3 about point W. Let E be the perpendicular bisector of segment WS. Let U be the rotation of point S by angle 11pi/12 around point W. Let D be the reflection of point U across point W. Let X be the reflection of line E through point U. P... | 18.21 | MATH |
[
{
"content": "LZ = 11. Let O be the rotation of point L by angle 5pi/6 around point Z. Let T be the rotation of point O by angle 5pi/6 around point Z. Point U is the midpoint of segment OZ. Let G be the line through point T perpendicular to segment OZ. Let S be the midpoint of segment TO. Line K passes through ... | 2.75 | MATH |
[
{
"content": "Let DY = 9. Point L is obtained by rotating point Y by angle 7pi/12 about point D. Let R be the midpoint of segment YD. Let G be the perpendicular bisector of segment RL. Point F is the reflection of point Y across line G. Point E is the reflection of point F across segment YD. Point M is the refl... | 39.22 | MATH |
[
{
"content": "PM = 9. Point B is the midpoint of segment PM. Line T is the perpendicular bisector of segment MB. Line O passes through point P parallel to line T. Point A is obtained by rotating point B by angle pi/6 about point M. Point Q is the midpoint of segment PA. Point G is the midpoint of segment AB. Po... | 4.1 | MATH |
[
{
"content": "Let IQ = 7. Point O is the midpoint of segment QI. Let R be the midpoint of segment OQ. Let D be the reflection of point R across point O. Let X be the line through point Q perpendicular to segment QR. Point B is the reflection of point R across line X. Let F be the midpoint of segment QB. Find th... | 6.12 | MATH |
[
{
"content": "RD = 5. Line F is the perpendicular bisector of segment DR. Point B is on line F with |BD| = 1. Line Y is the perpendicular bisector of segment BD. Point Q is the midpoint of segment BR. Point U is the reflection of point R across line Y. Let N be the midpoint of segment BQ. Point V is the midpoin... | 7.03 | MATH |
[
{
"content": "Let XY = 3. Let G be the perpendicular bisector of segment XY. Point U is obtained by rotating point X by angle 5pi/6 about point Y. Let F be the midpoint of segment XU. Point A is the reflection of point U across line G. Let T be the vector from point F to point X. Let W be point X translated by ... | 9.51 | MATH |
[
{
"content": "Let DU = 4. Point B is the midpoint of segment UD. Point S is the midpoint of segment BD. Point G is the reflection of point S across point U. Let W be the rotation of point S by angle 7pi/12 around point G. Point K is the midpoint of segment GW. Let O be the rotation of point D by angle 11pi/12 a... | 7.8 | MATH |
[
{
"content": "Let IY = 3. Point D is the midpoint of segment YI. Point Z is obtained by rotating point D by angle pi/12 about point Y. Point X is obtained by rotating point Z by angle 3pi/4 about point D. Let K be the midpoint of segment XD. Let Q be the midpoint of segment KI. Point J is the reflection of poin... | 0.96 | MATH |
[
{
"content": "QE = 9. Point L is the reflection of point Q across point E. Let Y be the midpoint of segment QE. Point R is the reflection of point Y across point L. Let O be the reflection of point Q across point R. Point I is the reflection of point E across point O. Point P is the reflection of point E across... | 63.0 | MATH |
[
{
"content": "Let TJ = 8. Point X is the midpoint of segment TJ. Let Q be the rotation of point X by angle 11pi/12 around point J. Let L be the angle bisector of angle XJT. Line P passes through point Q perpendicular to line L. Point C is the reflection of point X across line P. Point F is obtained by rotating ... | 14.82 | MATH |
[
{
"content": "FT = 3. Let M be the reflection of point F across point T. Point A is the midpoint of segment TM. Line K is the perpendicular bisector of segment FM. Point C is the reflection of point F across point A. Line P is the angle bisector of angle CMF. Point D is the reflection of point A across line K. ... | 5.85 | MATH |
[
{
"content": "Let GT = 1. Let P be the rotation of point T by angle 3pi/4 around point G. Let I be the reflection of point T across point G. Line L passes through point I perpendicular to segment GP. Point F is the reflection of point T across line L. Line C passes through point T perpendicular to segment GP. L... | 5.85 | MATH |
[
{
"content": "Let ZC = 7. Let R be the vector from point Z to point C. Let L be the midpoint of segment ZC. Point M is the reflection of point L across point C. Point P is the reflection of point C across point M. Let Y be the midpoint of segment PM. Let B be point Y translated by vector R. Let D be the perpend... | 2.8 | MATH |
[
{
"content": "IL = 4. Let T be the rotation of point I by angle 7pi/12 around point L. Point W is the reflection of point L across point I. Let P be the midpoint of segment IW. Let V be the line through points T and P. Point Y is the reflection of point I across line V. What is the distance between points Y and... | 3.51 | MATH |
[
{
"content": "PA = 1. Let N be the reflection of point P across point A. Line F is the perpendicular bisector of segment NP. Let O be the reflection of point N across point P. Let I be the reflection of point P across point O. Line V is the perpendicular bisector of segment PO. Let Q be the line through point I... | 19.2 | MATH |
[
{
"content": "Let MP = 6. Let W be the vector from point P to point M. Let A be the line through points P and M. Line F passes through point P perpendicular to line A. Line E passes through point M parallel to line F. Let L be the reflection of point P across point M. Line I is the reflection of line E across l... | 9.04 | MATH |
[
{
"content": "DV = 12. Let A be the rotation of point V by angle 11pi/12 around point D. Let R be the rotation of point V by angle pi/2 around point A. Point Z is the midpoint of segment VD. Point T is the midpoint of segment AR. Point N is the midpoint of segment VT. Let O be the midpoint of segment ZN. Point ... | 8.97 | MATH |
[
{
"content": "SL = 6. Point R is obtained by rotating point S by angle 5pi/6 about point L. Let G be the perpendicular bisector of segment SR. Point M is the midpoint of segment SL. Line V passes through point M parallel to line G. Point H is the reflection of point L across line V. Find the distance between po... | 11.69 | MATH |
[
{
"content": "RE = 9. Let S be the line through points E and R. Let T be the vector from point R to point E. Let L be point E translated by vector T. Point Y is obtained by rotating point R by angle 5pi/6 about point L. Let B be the reflection of point Y across point L. Point P is the reflection of point B acro... | 20.47 | MATH |
[
{
"content": "Let AM = 5. Let F be the midpoint of segment MA. Let P be the rotation of point A by angle 5pi/6 around point M. Line W is the perpendicular bisector of segment AF. Line I passes through points M and F. Line L passes through point P parallel to line W. Point R is the reflection of point M across l... | 4.96 | MATH |
[
{
"content": "Let BV = 7. Let T be the reflection of point B across point V. Let P be the line through points V and T. Line N passes through point T perpendicular to line P. Point Q is the reflection of point B across line N. What is the distance between points Q and T? Express your answer as a decimal number r... | 14.0 | MATH |
[
{
"content": "Let QV = 6. Let B be the reflection of point Q across point V. Point E is obtained by rotating point Q by angle pi about point B. Let U be the midpoint of segment BE. Point T is the reflection of point E across point Q. Let A be the rotation of point U by angle 7pi/12 around point E. Line Y is the... | 21.41 | MATH |
[
{
"content": "Let OK = 5. Let P be the perpendicular bisector of segment OK. Line C is the reflection of line P across point O. Let G be the line through point O parallel to line C. Let H be the line through point K parallel to line P. Let W be the vector from point O to point K. Point F is obtained by rotating... | 15.0 | MATH |
[
{
"content": "YH = 6. Let J be the vector from point H to point Y. Point F is the translation of point Y by vector J. Point D is obtained by rotating point H by angle 7pi/12 about point F. Let W be point D translated by vector J. Point Z is obtained by rotating point F by angle 11pi/12 about point Y. Let S be t... | 6.88 | MATH |
[
{
"content": "NP = 3. Let R be the vector from point N to point P. Let Y be point P translated by vector R. Line X is the perpendicular bisector of segment NP. Let Q be the line through point Y parallel to line X. Point O is the midpoint of segment PN. Let J be the perpendicular bisector of segment PY. Point V ... | 6.71 | MATH |
[
{
"content": "Let IG = 1. Let C be the perpendicular bisector of segment GI. Let A be the line through point G parallel to line C. Let K be the midpoint of segment IG. Point H is the reflection of point K across point I. Point Y is the reflection of point H across line A. Point L is obtained by rotating point H... | 5.22 | MATH |
[
{
"content": "YW = 4. Let K be the vector from point Y to point W. Let P be point W translated by vector K. Point N is obtained by rotating point Y by angle 3pi/4 about point W. Line D is the perpendicular bisector of segment YP. Point U is the reflection of point Y across point N. Point R is the reflection of ... | 0.79 | MATH |
[
{
"content": "KY = 3. Point C is obtained by rotating point K by angle pi/6 about point Y. Point Q is the reflection of point Y across point C. Point D is the reflection of point Y across point Q. Let T be the reflection of point K across point Q. Let W be the midpoint of segment DK. What is the distance betwee... | 3.08 | MATH |
[
{
"content": "Let JT = 4. Point R is obtained by rotating point T by angle 5pi/12 about point J. Line X passes through points T and J. Line O passes through point R parallel to line X. Let A be the midpoint of segment TJ. Let L be the midpoint of segment JR. Point D is the midpoint of segment LT. Let W be the p... | 8.73 | MATH |
[
{
"content": "CZ = 6. Let X be the midpoint of segment CZ. Point J is the midpoint of segment XC. Let G be the midpoint of segment XJ. Let M be the rotation of point Z by angle pi/12 around point J. Let Q be the midpoint of segment CG. Let D be the midpoint of segment GJ. Let K be the midpoint of segment DZ. Po... | 4.89 | MATH |
[
{
"content": "KP = 1. Point W is obtained by rotating point K by angle pi/6 about point P. Let L be the rotation of point K by angle 5pi/12 around point W. Let S be the angle bisector of angle PWL. Point X lies on line S at distance 8 from point W. Let N be the reflection of point L across point X. Point Q is t... | 1.96 | MATH |
[
{
"content": "HD = 5. Point T is obtained by rotating point H by angle pi/6 about point D. Let A be the line through points T and D. Let R be the reflection of point T across point H. Let P be the line through point D perpendicular to line A. Let M be the rotation of point H by angle pi/12 around point D. Point... | 3.94 | MATH |
[
{
"content": "Let IX = 10. Let B be the rotation of point I by angle 3pi/4 around point X. Point Q is obtained by rotating point X by angle pi/3 about point I. Line T is the angle bisector of angle QXB. Point P is the reflection of point I across line T. Point N is the reflection of point X across point B. Let ... | 50.37 | MATH |
[
{
"content": "Let JA = 1. Let Y be the rotation of point J by angle pi/4 around point A. Let L be the rotation of point A by angle pi/3 around point J. Point E is obtained by rotating point A by angle pi/6 about point Y. Line Q is the angle bisector of angle EJY. Let R be the rotation of point Y by angle 11pi/1... | 0.89 | MATH |
[
{
"content": "Let WZ = 9. Point D is the reflection of point W across point Z. Line Y is the perpendicular bisector of segment ZW. Point A is the midpoint of segment DZ. Let U be the vector from point D to point W. Point T is the reflection of point D across line Y. Point G is the translation of point T by vect... | 41.79 | MATH |
[
{
"content": "Let EQ = 10. Let H be the vector from point Q to point E. Let L be point E translated by vector H. Line B is the perpendicular bisector of segment LQ. Point U is on line B with |UE| = 12. Let R be the angle bisector of angle QLE. Point F is the midpoint of segment UL. Line X is the reflection of l... | 23.32 | MATH |
[
{
"content": "Let ZY = 3. Let K be the perpendicular bisector of segment YZ. Point P is on line K. Let T be the rotation of point Z by angle 3pi/4 around point Y. Point F is the reflection of point T across line K. Let L be the midpoint of segment PZ. Line G is the reflection of line K across point L. Point O i... | 3.0 | MATH |
[
{
"content": "CA = 7. Line G is the perpendicular bisector of segment CA. Line I is the reflection of line G across point C. Point P is the reflection of point A across line I. Point F is the reflection of point P across line G. Point Y is the reflection of point C across line I. Point M is the midpoint of segm... | 21.0 | MATH |
[
{
"content": "Let SP = 9. Point G is obtained by rotating point P by angle pi/3 about point S. Point U is the midpoint of segment SG. Line W is the angle bisector of angle GPU. Point V is the reflection of point U across line W. Let J be the reflection of point S across point P. Point L is the reflection of poi... | 25.62 | MATH |
[
{
"content": "QL = 6. Point S is obtained by rotating point Q by angle pi/4 about point L. Let E be the midpoint of segment SL. Line I is the angle bisector of angle LQE. Point V lies on segment EQ. Point X is the reflection of point L across segment VS. Point A is the reflection of point S across line I. Point... | 3.0 | MATH |
[
{
"content": "Let ON = 1. Let I be the perpendicular bisector of segment ON. Point T is on line I with |TN| = 8. Let S be the perpendicular bisector of segment NT. Line C passes through point T parallel to line S. Point Y is the reflection of point O across line C. Let X be the reflection of point N across poin... | 1.0 | MATH |
[
{
"content": "Let YZ = 8. Let A be the rotation of point Z by angle pi around point Y. Let Q be the reflection of point Y across point Z. Let S be the rotation of point A by angle pi/4 around point Y. Let T be the midpoint of segment AS. Point G is the reflection of point A across point Z. Point D is the reflec... | 16.0 | MATH |
[
{
"content": "RX = 5. Let M be the line through points X and R. Let E be the rotation of point X by angle 7pi/12 around point R. Let A be the reflection of point X across point E. Let J be the line through point E perpendicular to line M. Let Z be the midpoint of segment XE. Line V passes through point Z perpen... | 7.49 | MATH |
[
{
"content": "GY = 1. Line V is the perpendicular bisector of segment YG. Let U be the reflection of line V through point Y. Point F is the reflection of point Y across line U. Line S passes through points G and F. Point M is the midpoint of segment YF. Let N be the vector from point M to point G. Point A lies ... | 16.61 | MATH |
[
{
"content": "CA = 5. Point H is the reflection of point A across point C. Line D passes through points C and H. Line V passes through point A perpendicular to line D. Let L be the rotation of point H by angle pi/2 around point C. Point P is obtained by rotating point H by angle pi/3 about point A. Point E is t... | 11.47 | MATH |
[
{
"content": "Let OG = 5. Line Z passes through points O and G. Let P be the rotation of point O by angle pi/3 around point G. Line S is the perpendicular bisector of segment PO. Point N is the midpoint of segment PG. Let V be the line through point P parallel to line S. Lines Z and V intersect at point T. Find... | 0.52 | MATH |
[
{
"content": "SO = 6. Point W is the reflection of point O across point S. Line F is the angle bisector of angle SWO. Let C be the rotation of point W by angle pi/3 around point O. Let U be the midpoint of segment SC. Point R is the reflection of point U across line F. Let Z be the reflection of point U across ... | 16.7 | MATH |
[
{
"content": "RN = 4. Let Z be the midpoint of segment NR. Point F is obtained by rotating point N by angle pi/2 about point R. Let E be the rotation of point Z by angle 5pi/12 around point R. Let H be the midpoint of segment NZ. Point X is the reflection of point E across point Z. Line Q is the angle bisector ... | 5.52 | MATH |
[
{
"content": "CN = 10. Line I passes through point C perpendicular to segment CN. Point J is the reflection of point N across line I. Point Z is the midpoint of segment CN. Line E is the perpendicular bisector of segment CN. Let D be the rotation of point N by angle pi/6 around point Z. Point A is the reflectio... | 2.59 | MATH |
[
{
"content": "Let LG = 9. Point Z is the midpoint of segment GL. Let F be the midpoint of segment GZ. Point R is obtained by rotating point F by angle 11pi/12 about point Z. Let B be the vector from point R to point F. Let Q be the midpoint of segment GR. Let X be point Q translated by vector B. Let D be the ro... | 15.65 | MATH |
[
{
"content": "Let OJ = 11. Let B be the midpoint of segment JO. Let V be the midpoint of segment JB. Point K is obtained by rotating point V by angle pi/12 about point J. Point S is the reflection of point V across point O. Let W be the rotation of point O by angle 7pi/12 around point B. Point N is the midpoint... | 3.62 | MATH |
[
{
"content": "GR = 5. Line X is the perpendicular bisector of segment GR. Point A is on line X with |AG| = 7. Line W is the reflection of line X across point R. Let P be the line through point A parallel to segment GR. Point Q is the reflection of point R across line P. Point C is the reflection of point A acro... | 14.39 | MATH |
[
{
"content": "Let OE = 5. Let F be the rotation of point O by angle 7pi/12 around point E. Point C is the reflection of point F across segment EO. Line Z is the perpendicular bisector of segment FE. Point U is the midpoint of segment OF. Point P is the reflection of point U across segment EO. Let T be the vecto... | 26.29 | MATH |
[
{
"content": "Let OM = 2. Let J be the rotation of point O by angle pi/6 around point M. Let Y be the rotation of point J by angle 3pi/4 around point O. Let H be the angle bisector of angle YMJ. Line V is the reflection of line H across point Y. Line P is the reflection of line V across point O. Let Q be the ve... | 13.73 | MATH |
[
{
"content": "Let JV = 11. Let S be the vector from point J to point V. Let U be point V translated by vector S. Let L be the rotation of point J by angle 11pi/12 around point U. Let P be the line through points U and L. Point Y is on segment VJ. Point I is the midpoint of segment YU. Point O is the reflection ... | 0.52 | MATH |
[
{
"content": "YV = 10. Let W be the rotation of point Y by angle 3pi/4 around point V. Let X be the vector from point Y to point W. Point T is the translation of point W by vector X. Let J be the reflection of point W across point Y. Point A is the midpoint of segment VY. Let G be the line through point J perpe... | 6.99 | MATH |
[
{
"content": "Let BO = 11. Let C be the rotation of point B by angle pi/3 around point O. Point D is obtained by rotating point C by angle pi/12 about point B. Point N is the midpoint of segment OC. Point L is the reflection of point N across point O. Point K is the reflection of point B across segment DL. Poin... | 11.0 | MATH |
[
{
"content": "Let BI = 5. Point A is the midpoint of segment BI. Let K be the line through point B perpendicular to segment BA. Point N is obtained by rotating point B by angle pi about point I. Point F is the reflection of point N across line K. Line R is the perpendicular bisector of segment BA. Let P be the ... | 27.5 | MATH |
[
{
"content": "UE = 12. Point V is obtained by rotating point U by angle 3pi/4 about point E. Point H is the midpoint of segment UE. Let X be the midpoint of segment HV. Let D be the reflection of point X across point H. Find the distance between points D and H. Express your answer as a decimal number rounded to... | 8.39 | MATH |
[
{
"content": "Let DE = 9. Point V is obtained by rotating point E by angle 11pi/12 about point D. Point S is the midpoint of segment VE. Line M is the perpendicular bisector of segment ED. Let Y be the rotation of point V by angle pi/4 around point D. Let Z be the reflection of line M through point V. Point X i... | 31.93 | MATH |
[
{
"content": "Let RO = 3. Let F be the rotation of point R by angle 5pi/12 around point O. Point D is the midpoint of segment FR. Let I be the rotation of point O by angle 5pi/6 around point R. Let N be the midpoint of segment DO. Let Q be the midpoint of segment IR. Let E be the reflection of point I across po... | 5.19 | MATH |
[
{
"content": "Let PE = 1. Let O be the vector from point P to point E. Line I is the perpendicular bisector of segment PE. Point U is the translation of point E by vector O. Let B be the rotation of point P by angle pi/12 around point E. Point J is the reflection of point U across line I. Let W be the vector fr... | 2.88 | MATH |
[
{
"content": "KP = 12. Let R be the perpendicular bisector of segment PK. Point B is on line R with |BP| = 12. Point D is the reflection of point K across point P. Let O be the midpoint of segment PB. Let E be the midpoint of segment OD. Point W is the reflection of point E across point P. What is the length of... | 9.12 | MATH |
[
{
"content": "IW = 9. Point Y is the reflection of point W across point I. Point G is obtained by rotating point W by angle 2pi/3 about point I. Let C be the midpoint of segment GI. Let N be the rotation of point I by angle pi/12 around point G. Let P be the line through point W perpendicular to segment GY. Poi... | 8.83 | MATH |
[
{
"content": "HX = 5. Let J be the line through points H and X. Let Z be the rotation of point X by angle pi/6 around point H. Let I be the reflection of point X across point H. Point E is the reflection of point I across point Z. Line N is the perpendicular bisector of segment HI. Let T be the midpoint of segm... | 6.83 | MATH |
[
{
"content": "EK = 9. Let X be the reflection of point K across point E. Let Y be the rotation of point K by angle pi/4 around point X. Let P be the reflection of point Y across point K. Let G be the reflection of point K across point Y. Point A is the midpoint of segment KE. Point C is the reflection of point ... | 44.0 | MATH |
[
{
"content": "Let RA = 4. Point Z is obtained by rotating point R by angle 5pi/12 about point A. Line G passes through point Z perpendicular to segment RA. Line L passes through point A perpendicular to segment AZ. Let F be the reflection of point R across point A. Line D is the reflection of line G across poin... | 17.54 | MATH |
[
{
"content": "DV = 2. Point Z is obtained by rotating point D by angle 7pi/12 about point V. Point Q is the reflection of point V across point D. Let R be the reflection of point Z across point Q. Let X be the reflection of point Q across point V. Let B be the perpendicular bisector of segment RV. Point G is th... | 8.91 | MATH |
[
{
"content": "Let SG = 3. Let J be the midpoint of segment GS. Point V is obtained by rotating point S by angle 3pi/4 about point J. Let F be the angle bisector of angle GVS. Let I be the rotation of point S by angle 11pi/12 around point V. Point Y is the reflection of point I across segment VG. Line C is the r... | 2.77 | MATH |
[
{
"content": "Let VL = 6. Let P be the reflection of point L across point V. Point R is the midpoint of segment LV. Line M is the angle bisector of angle RVP. Let Z be the reflection of point R across point P. Point J is the reflection of point Z across line M. Let N be the rotation of point P by angle pi/6 aro... | 64.81 | MATH |
[
{
"content": "HD = 3. Point G is the reflection of point H across point D. Let S be the midpoint of segment GD. Let O be the perpendicular bisector of segment DH. Point C is the reflection of point G across line O. Point P is the midpoint of segment GS. What is the distance between points C and P? Express your ... | 8.25 | MATH |
[
{
"content": "Let FP = 2. Let I be the vector from point P to point F. Let G be the rotation of point F by angle pi around point P. Let E be the perpendicular bisector of segment GF. Let Z be the reflection of point F across point G. Let H be the perpendicular bisector of segment GP. Point M is the reflection o... | 8.78 | MATH |
[
{
"content": "NM = 10. Point T is the midpoint of segment MN. Point D is obtained by rotating point N by angle 5pi/6 about point M. Point F is the midpoint of segment DN. Point X is the reflection of point D across segment FT. Line K passes through points T and M. Let V be the line through point X perpendicular... | 11.18 | MATH |
[
{
"content": "Let SN = 1. Let K be the rotation of point S by angle 5pi/12 around point N. Let C be the midpoint of segment SN. Let B be the rotation of point C by angle 5pi/6 around point N. Point M is the midpoint of segment CK. Let T be the rotation of point B by angle 7pi/12 around point C. Let R be the ref... | 1.68 | MATH |
[
{
"content": "QA = 4. Point K is obtained by rotating point A by angle 2pi/3 about point Q. Let T be the perpendicular bisector of segment KQ. Line X passes through point Q parallel to line T. Let Z be the rotation of point Q by angle 5pi/12 around point K. Point H is the midpoint of segment KA. Let I be the li... | 5.83 | MATH |
[
{
"content": "JV = 4. Let U be the reflection of point J across point V. Let Z be the rotation of point U by angle 3pi/4 around point J. Line G passes through points J and Z. Let F be the perpendicular bisector of segment JV. Let R be the reflection of line G across line F. Lines G and R intersect at point O. P... | 11.76 | MATH |
[
{
"content": "WK = 6. Line B passes through points K and W. Point I is obtained by rotating point K by angle 7pi/12 about point W. Point Y is the midpoint of segment WK. Let J be the perpendicular bisector of segment YK. Let C be the line through points I and K. Line H passes through point K parallel to line J.... | 1.74 | MATH |
[
{
"content": "Let NW = 7. Let V be the rotation of point N by angle pi/6 around point W. Line G is the angle bisector of angle VWN. Let U be the angle bisector of angle WVN. Let O be the reflection of point V across point W. Line I is the reflection of line U across line G. Point Q is the reflection of point W ... | 10.38 | MATH |
[
{
"content": "TG = 12. Let V be the midpoint of segment GT. Let E be the rotation of point V by angle 7pi/12 around point T. Let O be the reflection of point T across point G. Point M is obtained by rotating point V by angle pi/3 about point T. Point Q is obtained by rotating point G by angle 2pi/3 about point ... | 36.64 | MATH |
[
{
"content": "LO = 7. Let F be the line through points O and L. Point M is obtained by rotating point L by angle pi about point O. Line R passes through point M perpendicular to line F. Let S be the angle bisector of angle LOM. Let P be the reflection of point L across point M. Line K passes through point P par... | 49.0 | MATH |
[
{
"content": "Let OW = 1. Point V is the midpoint of segment WO. Point P is obtained by rotating point W by angle pi about point O. Line I is the perpendicular bisector of segment WP. Line A is the reflection of line I across point V. Line Y is the reflection of line A across line I. Point U is on line A. Line ... | 4.0 | MATH |
[
{
"content": "AC = 1. Let W be the rotation of point A by angle pi/6 around point C. Let V be the reflection of point W across point C. Point Z is the midpoint of segment AW. Line K passes through point W parallel to segment AC. Point D is the midpoint of segment VC. Let X be the reflection of point V across po... | 3.31 | MATH |
[
{
"content": "XF = 7. Let D be the reflection of point F across point X. Let Z be the perpendicular bisector of segment XD. Line P passes through point D parallel to line Z. Let K be the line through point F perpendicular to segment XD. Point C lies on line K at distance 10 from point X. Point M lies on line P ... | 7.83 | MATH |
[
{
"content": "Let JZ = 6. Point R is the midpoint of segment JZ. Line F is the perpendicular bisector of segment ZR. Point Y is the midpoint of segment RZ. Point O is obtained by rotating point Z by angle pi/6 about point R. Let D be the midpoint of segment JR. Let L be the rotation of point O by angle 7pi/12 a... | 7.73 | MATH |
[
{
"content": "Let JH = 12. Point R is the reflection of point H across point J. Point K is the midpoint of segment RJ. Line A is the perpendicular bisector of segment KJ. Line D passes through point K parallel to line A. Point Q is the reflection of point H across line D. Point Z is the midpoint of segment QK. ... | 9.0 | MATH |
[
{
"content": "Let VZ = 6. Let R be the reflection of point V across point Z. Point K is obtained by rotating point Z by angle pi about point R. Let W be the midpoint of segment ZR. Let Q be the midpoint of segment WK. Let F be the perpendicular bisector of segment QV. Point X is the reflection of point Z across... | 7.5 | MATH |
[
{
"content": "Let KC = 2. Line H passes through points K and C. Let G be the reflection of point C across point K. Let E be the angle bisector of angle CKG. Line X is the reflection of line E across point C. Let F be the reflection of point C across point G. Point L lies on line X at distance 5 from point C. Li... | 11.42 | MATH |
[
{
"content": "Let YO = 1. Line J passes through points Y and O. Let H be the reflection of point Y across point O. Let F be the rotation of point Y by angle pi/3 around point H. Point D is obtained by rotating point F by angle pi/3 about point H. Point W is the midpoint of segment DY. Point B is the reflection ... | 11.0 | MATH |
[
{
"content": "YN = 10. Point Z is the reflection of point N across point Y. Let J be the perpendicular bisector of segment ZY. Let L be the reflection of line J through point Y. Point V is on line L with |VN| = 5. Line S is the perpendicular bisector of segment VZ. Point F is the reflection of point Y across li... | 21.38 | MATH |
[
{
"content": "MT = 1. Point X is the reflection of point T across point M. Let G be the rotation of point X by angle pi/2 around point M. Let L be the midpoint of segment TG. Let J be the reflection of point G across point T. Let C be the midpoint of segment XL. Point F is the reflection of point J across point... | 2.55 | MATH |
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