messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
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[
{
"content": "Let XG = 12. Let Z be the midpoint of segment XG. Let A be the rotation of point Z by angle 7pi/12 around point X. Point I is the reflection of point A across point G. Point H is the reflection of point Z across point A. Line P is the angle bisector of angle HGX. Point R is the reflection of point... | 20.96 | MATH |
[
{
"content": "TD = 7. Let N be the reflection of point T across point D. Let Y be the rotation of point N by angle 5pi/12 around point D. Let V be the reflection of point D across point Y. Let S be the line through points N and V. Let Z be the line through point Y parallel to line S. Point P is the reflection o... | 15.5 | MATH |
[
{
"content": "Let RT = 9. Point K is obtained by rotating point R by angle 7pi/12 about point T. Point V is obtained by rotating point K by angle 5pi/6 about point T. Let F be the rotation of point K by angle pi around point T. Point Q is the midpoint of segment VT. Let W be the midpoint of segment TR. Let L be... | 1.83 | MATH |
[
{
"content": "Let XF = 2. Let U be the midpoint of segment XF. Point K is obtained by rotating point F by angle 7pi/12 about point U. Line T passes through points F and K. Point M is the midpoint of segment XK. Point V is the reflection of point M across line T. Let P be the midpoint of segment UM. Find the dis... | 1.28 | MATH |
[
{
"content": "LX = 7. Let C be the perpendicular bisector of segment LX. Point A is on line C with |AL| = 8. Let W be the angle bisector of angle XLA. Point T is the reflection of point X across line W. Point D is the midpoint of segment TA. Let Q be the vector from point A to point D. Point P lies on line W. L... | 15.36 | MATH |
[
{
"content": "UQ = 9. Point D is the reflection of point Q across point U. Line N is the perpendicular bisector of segment DQ. Let V be the vector from point Q to point D. Let J be the line through point Q parallel to line N. Let S be the midpoint of segment QU. Line K is the perpendicular bisector of segment Q... | 32.45 | MATH |
[
{
"content": "KY = 4. Let B be the rotation of point Y by angle pi/12 around point K. Point R is the midpoint of segment KY. Point P is the reflection of point B across point K. Let M be the reflection of point P across point R. Let D be the reflection of point B across point R. Let X be the reflection of point... | 3.95 | MATH |
[
{
"content": "CA = 2. Point G is the midpoint of segment AC. Point T is obtained by rotating point G by angle 2pi/3 about point A. Let Z be the midpoint of segment TG. Point U is the reflection of point Z across point C. Let L be the midpoint of segment TU. What is the distance between points G and L? Express y... | 0.66 | MATH |
[
{
"content": "Let CH = 1. Line P is the perpendicular bisector of segment HC. Point N lies on line P at distance 10 from point C. Let M be the midpoint of segment NH. Let D be the reflection of line P through point H. Let B be the reflection of line D through point M. Let U be the perpendicular bisector of segm... | 1.23 | MATH |
[
{
"content": "Let DG = 1. Let P be the rotation of point D by angle pi/12 around point G. Let U be the midpoint of segment DP. Let Y be the midpoint of segment DG. Let Q be the line through points Y and G. Point W is the reflection of point U across line Q. What is the measure of angle YWU, in radians? Express ... | 1.31 | MATH |
[
{
"content": "WJ = 5. Point T is the midpoint of segment WJ. Line I is the perpendicular bisector of segment JW. Let P be the rotation of point T by angle 7pi/12 around point W. Let Q be the midpoint of segment JT. Point Z is the midpoint of segment QP. Line R passes through point Z parallel to line I. Let F be... | 3.33 | MATH |
[
{
"content": "YD = 9. Let S be the rotation of point Y by angle pi/12 around point D. Point F is the midpoint of segment YS. Let Z be the perpendicular bisector of segment YF. Point V is obtained by rotating point D by angle pi/6 about point F. Point Q is the reflection of point F across point Y. Line H passes ... | 15.63 | MATH |
[
{
"content": "Let BC = 6. Let G be the vector from point C to point B. Let O be the midpoint of segment BC. Let V be point B translated by vector G. Point M is obtained by rotating point V by angle 11pi/12 about point O. Point P is obtained by rotating point C by angle 5pi/12 about point V. Let Q be the reflect... | 12.54 | MATH |
[
{
"content": "Let VD = 6. Point A is the midpoint of segment VD. Point S is obtained by rotating point V by angle pi/6 about point A. Point F is the reflection of point S across segment VD. Point M is the midpoint of segment VS. Let T be the midpoint of segment MF. Find the length of segment TS. Express your an... | 1.88 | MATH |
[
{
"content": "Let VJ = 11. Line A passes through points V and J. Point Z is obtained by rotating point J by angle 5pi/12 about point V. Point U is the reflection of point Z across line A. Line W passes through points Z and J. Let B be the rotation of point Z by angle 7pi/12 around point U. Let X be the perpendi... | 37.97 | MATH |
[
{
"content": "LO = 2. Line Y is the perpendicular bisector of segment OL. Let E be the rotation of point L by angle 5pi/6 around point O. Point D is obtained by rotating point L by angle pi/2 about point O. Point G is the reflection of point D across point L. Point F is the midpoint of segment DO. Point I is th... | 10.92 | MATH |
[
{
"content": "HL = 4. Let I be the line through points H and L. Let X be the line through point L perpendicular to line I. Point M is obtained by rotating point L by angle 11pi/12 about point H. Line B passes through point M parallel to line X. Point R is the reflection of point H across point M. Lines I and B ... | 8.77 | MATH |
[
{
"content": "Let MJ = 10. Point N is the midpoint of segment MJ. Let I be the reflection of point J across point M. Let V be the rotation of point J by angle pi/6 around point N. Let T be the midpoint of segment NJ. Point Q is the midpoint of segment VI. Point Z is the reflection of point N across segment VI. ... | 3.01 | MATH |
[
{
"content": "Let ZM = 1. B is constructed so that MB = 1. Point H is the reflection of point M across point Z. Line X passes through points H and B. C is placed 1 units away from B. Point I is the reflection of point Z across line X. Point F is the midpoint of segment IC. Let A be the midpoint of segment CH. F... | 0.5 | MATH |
[
{
"content": "FU = 11. Let J be the rotation of point U by angle 11pi/12 around point F. Line N passes through points U and F. Point E is obtained by rotating point F by angle 3pi/4 about point J. Line Q passes through points E and U. Line Z is the reflection of line N across line Q. Let O be the reflection of ... | 60.8 | MATH |
[
{
"content": "WG = 11. Point S is the reflection of point G across point W. C is placed 11 units away from G. Let B be the reflection of point S across point G. Let Z be the reflection of point S across point B. Point O is the midpoint of segment ZC. Point E is the midpoint of segment CW. What is the distance b... | 38.5 | MATH |
[
{
"content": "Let ZI = 5. Point V is the reflection of point Z across point I. Let A be the reflection of point I across point V. Let E be the midpoint of segment IV. What is the distance between points A and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex ... | 7.5 | MATH |
[
{
"content": "Let UY = 7. Let O be the reflection of point Y across point U. Let G be the rotation of point O by angle 7pi/12 around point U. Let M be the midpoint of segment UG. Let W be the reflection of point O across point G. Point K is the midpoint of segment WG. Find the distance between points K and M. E... | 8.6 | MATH |
[
{
"content": "Let TX = 6. Point P is obtained by rotating point T by angle 5pi/6 about point X. Point J is the midpoint of segment XT. Let V be the midpoint of segment PX. Point K is the midpoint of segment VT. Let F be the midpoint of segment KT. Line L passes through point F perpendicular to segment PX. Let U... | 9.93 | MATH |
[
{
"content": "Let UB = 1. Point J is obtained by rotating point U by angle pi/4 about point B. Let Z be the reflection of point J across point U. Point V is the midpoint of segment BU. Line X is the angle bisector of angle ZBJ. Point H is the reflection of point V across line X. What is the distance between poi... | 1.17 | MATH |
[
{
"content": "OG = 5. Let V be the rotation of point G by angle pi around point O. Let M be the vector from point G to point V. Point W is the translation of point O by vector M. Let P be the rotation of point V by angle 5pi/6 around point G. Line D passes through points W and G. Point U is the midpoint of segm... | 5.2 | MATH |
[
{
"content": "Let QX = 6. Point V is the reflection of point X across point Q. Let Y be the angle bisector of angle XQV. Line B passes through point V perpendicular to line Y. Let E be the line through point V parallel to line Y. Let S be the vector from point X to point V. Line J is the perpendicular bisector ... | 13.5 | MATH |
[
{
"content": "NY = 11. Let L be the reflection of point Y across point N. Line A passes through points Y and L. Let U be the reflection of point Y across point L. Let X be the angle bisector of angle UNY. Point P is obtained by rotating point L by angle 5pi/12 about point Y. Line G passes through point P perpen... | 39.78 | MATH |
[
{
"content": "Let EY = 4. Point Q is the reflection of point E across point Y. Let B be the rotation of point Q by angle 5pi/12 around point E. Point O is the midpoint of segment YQ. Point R is the midpoint of segment YO. Point X is the reflection of point R across segment YB. Let C be the line through point O ... | 9.7 | MATH |
[
{
"content": "XE = 7. Let H be the rotation of point E by angle 11pi/12 around point X. Point W is obtained by rotating point X by angle pi about point H. Point K is the reflection of point X across point W. Point A is the reflection of point E across point W. Let O be the line through points A and W. Point C i... | 2.43 | MATH |
[
{
"content": "XJ = 4. Let C be the line through point J perpendicular to segment XJ. Let S be the rotation of point X by angle 5pi/12 around point J. Let Z be the rotation of point J by angle pi/6 around point X. Let R be the reflection of line C through point Z. Let P be the reflection of line C across line R.... | 12.16 | MATH |
[
{
"content": "Let FY = 6. Let A be the rotation of point Y by angle pi/12 around point F. Point M is the midpoint of segment FY. Let R be the reflection of point A across point M. Point U is the midpoint of segment MR. Point Z is the reflection of point F across point U. What is the length of segment ZA? Expres... | 4.04 | MATH |
[
{
"content": "KV = 12. Point Y is obtained by rotating point V by angle pi/2 about point K. Let P be the midpoint of segment YV. Let N be the midpoint of segment PK. Let W be the perpendicular bisector of segment KY. Let A be the line through point K parallel to line W. Point C is obtained by rotating point P b... | 9.84 | MATH |
[
{
"content": "Let ZB = 2. Point L is obtained by rotating point Z by angle 7pi/12 about point B. Let K be the midpoint of segment BL. Point S is the reflection of point K across segment LZ. Let F be the midpoint of segment ZK. Point V is the reflection of point K across segment SB. What is the distance between ... | 0.31 | MATH |
[
{
"content": "IY = 7. Let K be the vector from point I to point Y. Let A be point Y translated by vector K. Point M is obtained by rotating point Y by angle 5pi/6 about point I. Line E is the perpendicular bisector of segment YA. Point B is obtained by rotating point I by angle 3pi/4 about point Y. Let P be the... | 14.3 | MATH |
[
{
"content": "BI = 1. Let E be the vector from point B to point I. Let H be the reflection of point I across point B. Point V is the translation of point I by vector E. Line R is the perpendicular bisector of segment BH. Point Y is on line R with |YI| = 11. Let J be the reflection of line R through point V. Lin... | 35.85 | MATH |
[
{
"content": "HK = 4. Point Y is the reflection of point K across point H. Point I is the reflection of point K across point Y. Line L is the perpendicular bisector of segment KI. Let C be the reflection of point Y across point K. Point S lies on line L at distance 5 from point Y. Point O is the midpoint of seg... | 21.34 | MATH |
[
{
"content": "AV = 10. Point Y is the reflection of point A across point V. Point N is obtained by rotating point A by angle pi/2 about point V. Let K be the line through point Y perpendicular to segment AN. Point R is the reflection of point V across line K. Point S is the reflection of point R across segment ... | 0.79 | MATH |
[
{
"content": "Let VA = 9. Point J is the reflection of point A across point V. Let P be the rotation of point A by angle pi/6 around point J. Line D is the perpendicular bisector of segment JA. Let W be the reflection of point V across point A. Let O be the rotation of point W by angle 3pi/4 around point J. Poi... | 9.51 | MATH |
[
{
"content": "Let QX = 7. Point T is the reflection of point X across point Q. Point I is the reflection of point Q across point X. Point W is the midpoint of segment QT. Point B is the reflection of point X across point I. Let V be the rotation of point B by angle pi/3 around point Q. Let C be the rotation of ... | 40.71 | MATH |
[
{
"content": "YV = 11. Point K is obtained by rotating point Y by angle pi/3 about point V. Let F be the reflection of point Y across point V. Line I passes through points F and Y. Let A be the reflection of line I through point K. Point B is the reflection of point K across line I. Point O is the reflection of... | 55.0 | MATH |
[
{
"content": "Let BI = 2. Point M is the midpoint of segment BI. Point Y is the midpoint of segment MI. Let S be the rotation of point Y by angle pi/2 around point M. Let P be the rotation of point S by angle pi/12 around point B. Point F is obtained by rotating point Y by angle pi about point P. Let R be the l... | 4.89 | MATH |
[
{
"content": "Let EC = 6. Let X be the reflection of point E across point C. Point R is obtained by rotating point X by angle 3pi/4 about point E. Point U is the reflection of point R across point C. Line Y passes through points E and R. Point V is the reflection of point U across line Y. Let T be the midpoint ... | 29.39 | MATH |
[
{
"content": "PT = 1. Let X be the rotation of point P by angle 5pi/12 around point T. Point I is the reflection of point T across point X. Let A be the reflection of point P across point T. Line R is the angle bisector of angle IXA. Line U passes through points I and P. Line N passes through point T parallel t... | 3.22 | MATH |
[
{
"content": "Let VC = 7. Let O be the midpoint of segment VC. Let X be the reflection of point O across point V. Point Z is the midpoint of segment VX. Point D is the reflection of point Z across point O. Find the distance between points D and V. Express your answer as a decimal number rounded to 2 decimal pla... | 8.75 | MATH |
[
{
"content": "DO = 8. Line Q is the perpendicular bisector of segment OD. Point I lies on line Q at distance 3 from point D. Line S passes through point O parallel to line Q. Let F be the vector from point I to point O. Point A is the translation of point D by vector F. Point H is the reflection of point D acro... | 8.27 | MATH |
[
{
"content": "NX = 1. Let U be the vector from point N to point X. Let E be the rotation of point X by angle 7pi/12 around point N. Point B is obtained by rotating point E by angle 7pi/12 about point X. Let I be the rotation of point E by angle 7pi/12 around point B. Let H be point E translated by vector U. Let... | 1.12 | MATH |
[
{
"content": "Let JR = 7. Let H be the line through points J and R. Point B is obtained by rotating point R by angle pi/6 about point J. Point G is the midpoint of segment BR. Line F is the perpendicular bisector of segment JG. Let T be the reflection of line F across line H. Line D is the reflection of line H ... | 2.02 | MATH |
[
{
"content": "LX = 9. Let P be the vector from point X to point L. Let Q be point L translated by vector P. Let S be the rotation of point Q by angle 11pi/12 around point X. Let T be the perpendicular bisector of segment QL. Let G be the midpoint of segment XL. Point E is the reflection of point S across line T... | 40.16 | MATH |
[
{
"content": "Let EN = 3. Let V be the rotation of point N by angle pi/3 around point E. Let F be the rotation of point V by angle 3pi/4 around point E. Let H be the rotation of point E by angle pi/12 around point F. Line I passes through points H and E. Point G is the reflection of point E across point H. Line... | 7.46 | MATH |
[
{
"content": "Let TD = 8. Let J be the midpoint of segment TD. Let C be the perpendicular bisector of segment JT. Point U is on line C with |UJ| = 10. Point Q is the midpoint of segment DJ. Let I be the perpendicular bisector of segment QT. Line K is the reflection of line I across point U. Point V is obtained ... | 4.25 | MATH |
[
{
"content": "Let BE = 11. Let N be the line through points B and E. Point S is obtained by rotating point E by angle pi/2 about point B. Point T is the reflection of point S across line N. Point X lies on line N at distance 1 from point S. Point M is the midpoint of segment XT. Let L be the midpoint of segment... | 5.04 | MATH |
[
{
"content": "HP = 10. Point C is the reflection of point H across point P. Point L is obtained by rotating point P by angle 5pi/6 about point C. Point G is obtained by rotating point H by angle 7pi/12 about point L. Line B passes through points G and H. Point V is the reflection of point G across point C. Poin... | 109.81 | MATH |
[
{
"content": "Let MV = 1. Point F is the midpoint of segment MV. Let E be the angle bisector of angle MFV. Point U is on line E. Point B is the midpoint of segment MF. Let K be the midpoint of segment UV. Let C be the midpoint of segment BU. What is the distance between points K and C? Express your answer as a ... | 0.38 | MATH |
[
{
"content": "BV = 8. Let Q be the vector from point B to point V. Let X be the vector from point B to point V. Point G is the midpoint of segment BV. Let O be the rotation of point G by angle pi/12 around point V. Let M be point O translated by vector X. Point H is the translation of point V by vector Q. Point... | 11.66 | MATH |
[
{
"content": "Let FX = 2. Let K be the reflection of point X across point F. Point U is the midpoint of segment FX. Let S be the reflection of point X across point K. Point Q is obtained by rotating point K by angle pi/6 about point U. Let T be the midpoint of segment QU. Line J is the perpendicular bisector of... | 11.72 | MATH |
[
{
"content": "RF = 11. Let W be the rotation of point R by angle 7pi/12 around point F. Let T be the midpoint of segment RW. Let J be the midpoint of segment RT. Let RL = 8. Line X is the angle bisector of angle RJL. Line Z is the perpendicular bisector of segment WJ. Point D is the reflection of point T across... | 8.73 | MATH |
[
{
"content": "Let GC = 9. Let Y be the rotation of point G by angle pi around point C. Line U is the perpendicular bisector of segment YC. Point N lies on segment CY. Point I lies on line U at distance 8 from point G. Point A is the reflection of point G across line U. Let Q be the reflection of point I across ... | 15.69 | MATH |
[
{
"content": "Let WD = 8. Line N is the perpendicular bisector of segment WD. Point A is the midpoint of segment WD. Point U is the midpoint of segment DA. Line F is the reflection of line N across point W. Let G be the reflection of point U across point D. Let T be the rotation of point U by angle 11pi/12 arou... | 18.32 | MATH |
[
{
"content": "Let PD = 5. Point V is obtained by rotating point P by angle 5pi/6 about point D. Let I be the midpoint of segment VP. Point S is the midpoint of segment VD. Point O is the reflection of point D across point I. Find the distance between points S and O. Express your answer as a decimal number round... | 3.1 | MATH |
[
{
"content": "Let JE = 3. Let X be the rotation of point E by angle 3pi/4 around point J. Let B be the rotation of point X by angle 3pi/4 around point E. Let D be the reflection of point X across point B. Point T is the reflection of point J across point B. Let R be the reflection of point T across point J. Let... | 22.97 | MATH |
[
{
"content": "NI = 10. Let H be the midpoint of segment NI. Line C is the perpendicular bisector of segment IN. Point P is obtained by rotating point H by angle pi/2 about point N. Point W is obtained by rotating point H by angle pi/3 about point N. Point X is the reflection of point N across point P. Let Y be ... | 13.23 | MATH |
[
{
"content": "Let DF = 6. Let X be the midpoint of segment FD. Point Z is obtained by rotating point X by angle pi/12 about point D. Let K be the reflection of point X across point D. Point B is the reflection of point D across segment XZ. Line L is the perpendicular bisector of segment KD. Point I is the refle... | 0.26 | MATH |
[
{
"content": "XO = 3. Point W is the reflection of point X across point O. Point A is the reflection of point X across point W. Let P be the rotation of point O by angle 7pi/12 around point W. Line D passes through point A perpendicular to segment XW. Let B be the reflection of point P across point W. Point H i... | 7.6 | MATH |
[
{
"content": "Let JS = 4. Let B be the rotation of point J by angle pi/3 around point S. Let C be the midpoint of segment JS. Let G be the rotation of point B by angle pi/4 around point J. Let L be the rotation of point B by angle 5pi/12 around point C. Let F be the perpendicular bisector of segment BG. Let W b... | 4.44 | MATH |
[
{
"content": "YP = 2. Let M be the reflection of point Y across point P. Point R is the midpoint of segment YP. Let Q be the rotation of point Y by angle 3pi/4 around point R. Let V be the perpendicular bisector of segment QP. Line U is the perpendicular bisector of segment MQ. Let L be the midpoint of segment ... | 1.25 | MATH |
[
{
"content": "CM = 2. Let U be the line through points M and C. Let X be the rotation of point M by angle pi/6 around point C. Let B be the reflection of line U through point X. Point N is the reflection of point X across line B. Let W be the line through points M and X. Lines B and W intersect at point R. What... | 1.04 | MATH |
[
{
"content": "Let LD = 2. Let F be the line through points L and D. Let M be the reflection of point L across point D. Point I is on line F. Point H is on line F with |HI| = 8. Point S lies on line F at distance 10 from point I. Let Y be the perpendicular bisector of segment SD. Point G is on line Y with |GH| =... | 2.0 | MATH |
[
{
"content": "JB = 6. Point S is obtained by rotating point J by angle pi/3 about point B. Let E be the rotation of point S by angle pi/4 around point B. Let U be the midpoint of segment SJ. Line F passes through point J perpendicular to segment UB. Point N is the reflection of point E across line F. Line V pas... | 2.98 | MATH |
[
{
"content": "LY = 1. Point P is obtained by rotating point L by angle pi about point Y. Let E be the rotation of point Y by angle 3pi/4 around point P. Let G be the line through points E and L. Let F be the line through point Y parallel to line G. Let I be the line through points L and P. Point J is the reflec... | 20.25 | MATH |
[
{
"content": "Let QW = 1. Let V be the midpoint of segment WQ. Point N is obtained by rotating point Q by angle pi/4 about point W. Let M be the midpoint of segment NV. Let R be the rotation of point W by angle 11pi/12 around point N. Point B is the reflection of point N across point R. Point C is the reflectio... | 1.49 | MATH |
[
{
"content": "GS = 8. Let K be the reflection of point G across point S. Let D be the midpoint of segment GS. Let F be the angle bisector of angle GDS. Point R is the midpoint of segment KD. Point Y is the midpoint of segment SR. Let Q be the reflection of line F through point Y. Point O lies on line Q. Point A... | 20.0 | MATH |
[
{
"content": "Let OF = 5. Point N is the reflection of point F across point O. Let C be the vector from point F to point O. Let Q be the perpendicular bisector of segment FO. Point Y is the translation of point N by vector C. Let L be the reflection of point Y across point O. Line J passes through point F paral... | 7.94 | MATH |
[
{
"content": "IN = 12. Point E is obtained by rotating point I by angle 5pi/6 about point N. Let X be the midpoint of segment EN. Line A passes through point X perpendicular to segment IE. Point D is the midpoint of segment EX. Point O is obtained by rotating point D by angle 11pi/12 about point I. Let T be the... | 38.24 | MATH |
[
{
"content": "Let WF = 7. Let X be the vector from point F to point W. Point E is the translation of point W by vector X. Point I is obtained by rotating point W by angle pi/4 about point F. Let D be the rotation of point W by angle 11pi/12 around point E. Line Y passes through points W and D. Point G is the re... | 4.72 | MATH |
[
{
"content": "Let KM = 5. Let V be the reflection of point M across point K. Let I be the reflection of point K across point V. Let P be the vector from point M to point I. Line C is the angle bisector of angle KVI. Point J is obtained by rotating point K by angle 5pi/12 about point M. Let U be point J translat... | 19.4 | MATH |
[
{
"content": "Let JE = 8. Point W is obtained by rotating point E by angle pi/3 about point J. Point N is the midpoint of segment EJ. Point V is the reflection of point W across point E. Point B is the reflection of point V across point W. Point G is the midpoint of segment NB. Point L is the reflection of poin... | 6.3 | MATH |
[
{
"content": "Let ML = 2. Point G is obtained by rotating point M by angle 2pi/3 about point L. Point I is the midpoint of segment LG. Point T is the reflection of point I across point M. Point D is the reflection of point T across point I. Point F is the midpoint of segment ML. Let S be the reflection of point... | 5.76 | MATH |
[
{
"content": "Let KS = 12. Let O be the rotation of point K by angle 5pi/6 around point S. Line W is the angle bisector of angle KSO. Point B is obtained by rotating point K by angle pi about point O. Let F be the line through point B parallel to line W. Let A be the reflection of point K across point B. Let I ... | 63.92 | MATH |
[
{
"content": "QG = 7. Point B is obtained by rotating point Q by angle 2pi/3 about point G. Line I is the perpendicular bisector of segment GQ. Let J be the reflection of line I through point G. Let C be the reflection of line J across line I. Line M passes through point Q parallel to segment BG. Point N is the... | 25.24 | MATH |
[
{
"content": "Let PN = 9. Point L is the reflection of point N across point P. Point W is obtained by rotating point L by angle 5pi/6 about point N. Point S is the midpoint of segment NW. Line J is the angle bisector of angle WPS. Point R is the midpoint of segment LW. Let O be the line through point W perpendi... | 42.52 | MATH |
[
{
"content": "Let BH = 11. Line P passes through points H and B. Point G is obtained by rotating point B by angle 5pi/6 about point H. Let M be the reflection of point H across point B. Point I is the reflection of point G across line P. Let F be the midpoint of segment MI. Let U be the reflection of point H ac... | 11.0 | MATH |
[
{
"content": "EC = 8. Let Q be the perpendicular bisector of segment CE. Let A be the rotation of point E by angle 5pi/12 around point C. Line V passes through point E parallel to line Q. Let I be the reflection of line V across line Q. Let K be the rotation of point E by angle 11pi/12 around point C. Point P i... | 32.3 | MATH |
[
{
"content": "RC = 2. Let B be the reflection of point C across point R. Line Z passes through points B and R. Point E is obtained by rotating point C by angle pi/4 about point R. Let U be the vector from point R to point B. Point A is the translation of point E by vector U. Let N be the line through point E pa... | 1.45 | MATH |
[
{
"content": "Let OG = 7. Let P be the midpoint of segment GO. Let X be the rotation of point O by angle 5pi/6 around point G. Point R is the midpoint of segment PX. Point M is obtained by rotating point G by angle pi/6 about point X. Let I be the midpoint of segment RX. Point T is the reflection of point O acr... | 12.35 | MATH |
[
{
"content": "Let HK = 7. Let M be the rotation of point H by angle pi/2 around point K. Let D be the midpoint of segment KH. Let I be the perpendicular bisector of segment DH. Line N is the reflection of line I across point K. Point L is the reflection of point M across line N. Find the distance between points... | 18.85 | MATH |
[
{
"content": "VZ = 8. Point K is the reflection of point V across point Z. Point E is obtained by rotating point V by angle 2pi/3 about point K. Let R be the vector from point V to point K. Let B be point E translated by vector R. Let F be the rotation of point Z by angle pi/3 around point V. Let T be the refle... | 10.39 | MATH |
[
{
"content": "RQ = 11. Let D be the rotation of point Q by angle 11pi/12 around point R. Line B is the angle bisector of angle QDR. Let Y be the midpoint of segment DQ. Point N is the reflection of point Y across line B. Point F is the midpoint of segment YN. What is the distance between points N and F? Express... | 0.71 | MATH |
[
{
"content": "DW = 5. Let O be the rotation of point W by angle pi/2 around point D. Let I be the rotation of point D by angle pi/3 around point W. Let Q be the angle bisector of angle IWO. Point M is the midpoint of segment WO. Line P passes through point I perpendicular to line Q. Line S is the perpendicular ... | 7.5 | MATH |
[
{
"content": "Let SH = 2. Point Y is obtained by rotating point S by angle 5pi/12 about point H. Point R is obtained by rotating point S by angle 2pi/3 about point H. Let D be the rotation of point Y by angle 2pi/3 around point R. Point T is the reflection of point Y across point R. Let M be the reflection of p... | 3.91 | MATH |
[
{
"content": "LE = 7. Let V be the midpoint of segment LE. Let S be the perpendicular bisector of segment VE. Line H passes through point E perpendicular to line S. Point J is obtained by rotating point L by angle pi/12 about point E. Line Z is the perpendicular bisector of segment EJ. Point O is the reflection... | 10.62 | MATH |
[
{
"content": "Let IH = 1. Point E is obtained by rotating point H by angle 7pi/12 about point I. Let X be the reflection of point I across point E. Let Z be the line through points H and X. Line L passes through point H perpendicular to line Z. Point W is the reflection of point X across line L. Find the distan... | 4.91 | MATH |
[
{
"content": "Let FQ = 7. Let X be the line through points Q and F. Point D is obtained by rotating point Q by angle 5pi/6 about point F. Point R is obtained by rotating point D by angle pi/12 about point F. Point W is obtained by rotating point F by angle pi/4 about point R. Let S be the reflection of line X t... | 11.97 | MATH |
[
{
"content": "Let GU = 9. Let P be the midpoint of segment GU. Let X be the midpoint of segment PU. Point I is obtained by rotating point X by angle pi/6 about point P. Let E be the perpendicular bisector of segment XU. Point T is the reflection of point G across line E. Line S passes through point P parallel t... | 9.51 | MATH |
[
{
"content": "Let WY = 12. Let C be the reflection of point Y across point W. Let D be the midpoint of segment YW. Point R is obtained by rotating point C by angle 5pi/6 about point D. Point K is the reflection of point C across point D. Let O be the midpoint of segment YK. Let J be the midpoint of segment OR. ... | 10.15 | MATH |
[
{
"content": "Let KV = 8. Let I be the rotation of point K by angle pi/6 around point V. Let T be the rotation of point K by angle 7pi/12 around point I. Point C is the reflection of point I across point T. Point A is the reflection of point C across segment KV. Point G is the reflection of point T across segme... | 4.14 | MATH |
[
{
"content": "Let QD = 1. Point Y is the midpoint of segment DQ. Point N is obtained by rotating point Q by angle 3pi/4 about point Y. Point O is the reflection of point Q across point D. Let V be the reflection of point O across point N. Point W is the reflection of point V across point Q. Point P is the refle... | 1.93 | MATH |
[
{
"content": "Let UW = 11. Point X is the reflection of point W across point U. Point I is obtained by rotating point W by angle pi/12 about point X. Let K be the midpoint of segment IU. Point R is the reflection of point U across segment KX. Let E be the midpoint of segment RI. Let H be the midpoint of segment... | 2.77 | MATH |
[
{
"content": "Let LX = 4. Point T is the midpoint of segment LX. Let U be the vector from point T to point X. Point P is obtained by rotating point L by angle 5pi/6 about point X. Point C is the translation of point X by vector U. Point Z is the midpoint of segment XP. Point J is the reflection of point Z acros... | 1.65 | MATH |
[
{
"content": "Let UM = 5. Let X be the midpoint of segment MU. Let C be the perpendicular bisector of segment UX. Point F is the reflection of point M across line C. Let D be the rotation of point M by angle 3pi/4 around point F. Line L is the perpendicular bisector of segment MU. Let I be the midpoint of segme... | 6.93 | MATH |
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