messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let YQ = 7. Point T is obtained by rotating point Y by angle 7pi/12 about point Q. Line O is the angle bisector of angle TYQ. Point R is the midpoint of segment QT. Point Z is the reflection of point R across point T. Point E is the reflection of point R across line O. Let F be the reflection of p... | 11.62 | MATH |
[
{
"content": "Let XQ = 3. Let E be the midpoint of segment QX. Point P is the midpoint of segment XE. Let V be the vector from point Q to point E. Point U is obtained by rotating point X by angle 2pi/3 about point Q. Point J is obtained by rotating point X by angle pi/6 about point U. Let B be the reflection of... | 8.73 | MATH |
[
{
"content": "FR = 12. Let G be the line through points F and R. Point D is on line G with |DF| = 12. Let B be the midpoint of segment DF. Let C be the rotation of point B by angle pi/3 around point D. Let K be the rotation of point B by angle pi/12 around point D. Point L is obtained by rotating point C by ang... | 17.43 | MATH |
[
{
"content": "LR = 8. Let H be the midpoint of segment RL. Let W be the angle bisector of angle HLR. Point F is obtained by rotating point H by angle 5pi/6 about point L. Let M be the reflection of line W through point F. Let K be the rotation of point H by angle pi/3 around point R. Let V be the reflection of ... | 57.26 | MATH |
[
{
"content": "OH = 12. Point A is obtained by rotating point H by angle 11pi/12 about point O. Point W is obtained by rotating point O by angle 5pi/12 about point A. Point N is the midpoint of segment AH. Point X is the reflection of point W across segment AH. Let E be the reflection of point N across point A. ... | 19.87 | MATH |
[
{
"content": "Let IV = 8. Let R be the reflection of point I across point V. Let J be the perpendicular bisector of segment VR. Point N is the reflection of point I across line J. Let G be the midpoint of segment IV. Find the distance between points G and N. Express your answer as a decimal number rounded to 2 ... | 20.0 | MATH |
[
{
"content": "EP = 4. Let H be the reflection of point P across point E. Point C is obtained by rotating point H by angle 5pi/12 about point E. Line T is the angle bisector of angle CEP. Line J is the reflection of line T across point C. Point U is on line J with |UC| = 12. Let W be the midpoint of segment CE. ... | 6.21 | MATH |
[
{
"content": "Let EZ = 9. Let A be the rotation of point E by angle pi/12 around point Z. Let X be the vector from point Z to point E. Let T be the angle bisector of angle ZEA. Let W be the reflection of line T through point A. Let K be the perpendicular bisector of segment AZ. Line N passes through point E per... | 31.58 | MATH |
[
{
"content": "SG = 12. Let W be the midpoint of segment GS. Let X be the rotation of point W by angle pi/6 around point S. Point T is obtained by rotating point S by angle 2pi/3 about point G. Let V be the midpoint of segment SX. Let A be the reflection of point T across point G. Point J is the midpoint of segm... | 3.67 | MATH |
[
{
"content": "EM = 1. Point D is the reflection of point E across point M. Point I is obtained by rotating point M by angle pi/6 about point E. Point N is the reflection of point D across point I. Let B be the line through points N and E. Let A be the midpoint of segment MI. Let F be the line through point A pa... | 2.9 | MATH |
[
{
"content": "Let GQ = 8. Let V be the rotation of point Q by angle 7pi/12 around point G. Let N be the reflection of point Q across point G. Let P be the rotation of point Q by angle 5pi/12 around point G. Let S be the angle bisector of angle PVN. Point E is the reflection of point G across line S. Point I is ... | 6.69 | MATH |
[
{
"content": "EQ = 10. Point O is obtained by rotating point Q by angle 2pi/3 about point E. Point K is the reflection of point Q across point E. Point V is the reflection of point O across point E. Point D is the midpoint of segment KO. Let A be the line through point V perpendicular to segment VD. Point L is ... | 36.06 | MATH |
[
{
"content": "Let QW = 3. Let X be the reflection of point Q across point W. Let M be the midpoint of segment XW. Point J is obtained by rotating point Q by angle pi/6 about point M. Line F is the angle bisector of angle XWQ. Let B be the midpoint of segment WM. Point I is the reflection of point J across line ... | 6.82 | MATH |
[
{
"content": "Let TC = 2. Point Y is the reflection of point C across point T. Let E be the line through points T and C. Line H passes through point C perpendicular to line E. Point M is obtained by rotating point C by angle pi/12 about point T. Let W be the midpoint of segment MY. Point B is the reflection of ... | 1.18 | MATH |
[
{
"content": "DF = 6. Point T is the midpoint of segment DF. Let J be the midpoint of segment TD. Point P is the midpoint of segment FJ. Let N be the rotation of point F by angle pi/4 around point T. Point W is obtained by rotating point T by angle 5pi/12 about point P. Let Q be the midpoint of segment PN. Poin... | 14.4 | MATH |
[
{
"content": "BW = 11. Let P be the midpoint of segment WB. Let Z be the rotation of point P by angle 11pi/12 around point B. Let H be the angle bisector of angle ZWB. Point E is obtained by rotating point P by angle 3pi/4 about point Z. Point T is on line H. Point I is the midpoint of segment BT. Point O is th... | 16.23 | MATH |
[
{
"content": "Let SM = 5. Let A be the rotation of point M by angle pi/3 around point S. Let W be the vector from point A to point M. Point B is the midpoint of segment SM. Point U is obtained by rotating point B by angle 5pi/12 about point S. Let F be point M translated by vector W. Let Q be the perpendicular ... | 16.06 | MATH |
[
{
"content": "Let PM = 12. Line A is the perpendicular bisector of segment MP. Let B be the line through point M parallel to line A. Let L be the reflection of line B across line A. Point S is the reflection of point M across line L. Let W be the midpoint of segment SP. Let E be the rotation of point W by angle... | 4.2 | MATH |
[
{
"content": "VS = 10. Line M is the perpendicular bisector of segment VS. Point J is obtained by rotating point V by angle pi/4 about point S. Let X be the rotation of point S by angle pi/6 around point V. Let I be the rotation of point S by angle pi/3 around point X. Let Y be the reflection of point I across ... | 55.5 | MATH |
[
{
"content": "Let BN = 12. Point K is obtained by rotating point B by angle pi/3 about point N. Line J is the angle bisector of angle NBK. Point T is the reflection of point B across point N. Let C be the reflection of line J through point T. Point X is the reflection of point N across line C. Let Q be the midp... | 12.0 | MATH |
[
{
"content": "VS = 11. Let X be the midpoint of segment VS. Point H is obtained by rotating point X by angle pi/6 about point S. Point O is the midpoint of segment VH. Point M is obtained by rotating point O by angle 3pi/4 about point X. Point Z is obtained by rotating point X by angle pi/3 about point S. Let Q... | 7.44 | MATH |
[
{
"content": "VO = 5. Point U is the midpoint of segment VO. Let C be the rotation of point V by angle pi/4 around point U. Let P be the rotation of point C by angle 3pi/4 around point O. Point F is obtained by rotating point C by angle pi/12 about point V. Line T is the angle bisector of angle PCF. Let S be th... | 2.51 | MATH |
[
{
"content": "PJ = 9. Point M is obtained by rotating point J by angle pi/2 about point P. Let T be the perpendicular bisector of segment PJ. Let L be the line through point M parallel to line T. Let W be the midpoint of segment MJ. Line R passes through point W parallel to segment PJ. Point O is the intersecti... | 0.79 | MATH |
[
{
"content": "JH = 8. Let F be the rotation of point H by angle 5pi/6 around point J. Point K is obtained by rotating point J by angle 5pi/6 about point F. Point M is obtained by rotating point K by angle pi/3 about point H. Point D is the midpoint of segment HM. Let T be the reflection of point F across point ... | 48.78 | MATH |
[
{
"content": "AM = 9. Point O is obtained by rotating point M by angle 7pi/12 about point A. AL = 9. Let F be the rotation of point A by angle 11pi/12 around point O. Let T be the line through points A and O. Line P passes through point F parallel to line T. Point K is the reflection of point A across line P. P... | 9.0 | MATH |
[
{
"content": "MP = 1. Line J is the perpendicular bisector of segment PM. Point D is on line J with |DP| = 2. Point O is obtained by rotating point P by angle pi/3 about point D. Let G be the vector from point P to point O. Let N be the reflection of point O across point P. Let Q be the line through points N an... | 8.66 | MATH |
[
{
"content": "QS = 2. Let V be the rotation of point Q by angle 7pi/12 around point S. Point D is the reflection of point V across segment QS. Point Z is the reflection of point D across point S. Point C is the midpoint of segment QS. Let X be the midpoint of segment CZ. Point J is the reflection of point X acr... | 1.93 | MATH |
[
{
"content": "YE = 6. Let T be the reflection of point E across point Y. Let W be the reflection of point E across point T. Point R is obtained by rotating point Y by angle 3pi/4 about point W. Line C passes through points R and W. Let K be the perpendicular bisector of segment TE. Line L is the reflection of l... | 21.63 | MATH |
[
{
"content": "Let FQ = 12. Point I is obtained by rotating point Q by angle 2pi/3 about point F. Let U be the reflection of point F across point Q. Line E is the perpendicular bisector of segment FI. Point G is the reflection of point Q across line E. Line Z is the angle bisector of angle UFQ. Let V be the rota... | 21.22 | MATH |
[
{
"content": "Let HF = 9. Line S is the perpendicular bisector of segment FH. Point I is obtained by rotating point H by angle pi about point F. Let R be the vector from point H to point I. Line G is the angle bisector of angle HFI. Let A be the midpoint of segment FH. Let J be point I translated by vector R. P... | 27.04 | MATH |
[
{
"content": "Let AP = 5. Point M is the midpoint of segment AP. Let X be the midpoint of segment AM. Let O be the rotation of point X by angle pi/3 around point M. Line S is the perpendicular bisector of segment OX. Line W is the angle bisector of angle XAM. Point C is the reflection of point A across line S. ... | 3.31 | MATH |
[
{
"content": "Let RH = 2. Point S is the reflection of point H across point R. Let C be the midpoint of segment RS. Let I be the rotation of point R by angle 2pi/3 around point C. Let E be the reflection of point R across point S. Point G is the reflection of point I across point C. Let A be the midpoint of seg... | 1.01 | MATH |
[
{
"content": "Let NY = 12. Point M is the reflection of point Y across point N. Point C is the midpoint of segment NM. Point J is the reflection of point M across point Y. Line O passes through point N perpendicular to segment NM. Point Q is obtained by rotating point Y by angle pi/3 about point C. Let Z be the... | 60.0 | MATH |
[
{
"content": "Let KW = 12. Line A is the perpendicular bisector of segment KW. Let P be the rotation of point K by angle pi/4 around point W. Line Z is the angle bisector of angle PKW. Line T is the reflection of line A across line Z. Line Y passes through point W parallel to line A. Let M be the midpoint of se... | 10.6 | MATH |
[
{
"content": "SE = 4. Point H is the reflection of point E across point S. Let I be the rotation of point S by angle 11pi/12 around point H. Point A is the midpoint of segment SE. Point C is the reflection of point I across segment HE. Point P is the midpoint of segment CA. Let T be the reflection of point P ac... | 3.77 | MATH |
[
{
"content": "IA = 4. Let G be the rotation of point I by angle 5pi/12 around point A. Point E is the midpoint of segment AI. Let L be the angle bisector of angle GAE. Point Q is obtained by rotating point G by angle pi/3 about point E. Let C be the rotation of point Q by angle pi/3 around point A. Line N is th... | 8.57 | MATH |
[
{
"content": "KY = 5. Let O be the perpendicular bisector of segment KY. Line X passes through point K parallel to line O. Let D be the rotation of point Y by angle pi/12 around point K. Point S is the reflection of point D across line X. Point A is the reflection of point D across line O. Point I is the reflec... | 19.19 | MATH |
[
{
"content": "Let NF = 1. Let R be the midpoint of segment FN. Point Y is obtained by rotating point F by angle 7pi/12 about point R. Point Q is the midpoint of segment YR. Point E is the reflection of point F across segment NY. Find the length of segment QE. Express your answer as a decimal number rounded to 2... | 1.0 | MATH |
[
{
"content": "JR = 12. Let K be the midpoint of segment RJ. Line A is the perpendicular bisector of segment RK. Point W lies on line A at distance 1 from point R. Line E passes through point K perpendicular to segment RJ. Let C be the reflection of point J across point W. Line V is the reflection of line E acro... | 9.12 | MATH |
[
{
"content": "Let BE = 11. Let G be the line through points B and E. Let P be the line through point B perpendicular to line G. Point N lies on line P at distance 7 from point E. Let X be the reflection of point N across point B. Point I is the reflection of point E across point X. Let W be the midpoint of segm... | 5.91 | MATH |
[
{
"content": "Let EY = 7. Let S be the midpoint of segment EY. Let K be the vector from point S to point Y. Line X is the perpendicular bisector of segment YS. Point H is the translation of point Y by vector K. Point Z is on line X with |ZH| = 9. Let L be the midpoint of segment SZ. Let F be the midpoint of seg... | 2.29 | MATH |
[
{
"content": "SB = 9. Point W is the midpoint of segment SB. Let P be the midpoint of segment BW. Line V is the perpendicular bisector of segment SW. Line Y is the reflection of line V across point W. Let D be the reflection of point S across point P. Point I lies on line Y at distance 9 from point W. Let M be ... | 14.4 | MATH |
[
{
"content": "Let QC = 9. Let I be the reflection of point C across point Q. Let B be the rotation of point Q by angle 5pi/6 around point I. Let G be the midpoint of segment BI. Let H be the reflection of point I across point B. Let S be the angle bisector of angle BQC. Point R is obtained by rotating point H b... | 2.5 | MATH |
[
{
"content": "JH = 10. Let B be the midpoint of segment HJ. Point T is obtained by rotating point H by angle 5pi/6 about point J. Let V be the midpoint of segment TB. Let I be the rotation of point T by angle pi/3 around point J. Point D is the midpoint of segment HV. Let W be the midpoint of segment IJ. Line C... | 11.57 | MATH |
[
{
"content": "OP = 7. Let A be the vector from point O to point P. Point F is the translation of point P by vector A. Point M is the translation of point F by vector A. Let W be the rotation of point M by angle 2pi/3 around point P. Point L is the midpoint of segment FW. Let S be the midpoint of segment LP. Seg... | 8.74 | MATH |
[
{
"content": "OF = 9. Point H is obtained by rotating point O by angle 5pi/6 about point F. Line A is the angle bisector of angle FHO. Point X is the reflection of point O across line A. Line C passes through point H perpendicular to line A. Point G is the reflection of point X across line C. Let T be the midpo... | 2.27 | MATH |
[
{
"content": "DR = 11. Line F is the perpendicular bisector of segment RD. Let W be the midpoint of segment RD. Line I is the perpendicular bisector of segment WD. Point P is on line I with |PW| = 6. Point Z is the midpoint of segment PD. Point V is the midpoint of segment WZ. Let A be the line through point Z ... | 2.52 | MATH |
[
{
"content": "Let WC = 10. Let D be the reflection of point C across point W. Let A be the perpendicular bisector of segment CD. Point Q is obtained by rotating point W by angle 7pi/12 about point C. Point H is obtained by rotating point D by angle pi/4 about point Q. Point J is obtained by rotating point W by ... | 9.71 | MATH |
[
{
"content": "FH = 3. Line B passes through point F perpendicular to segment HF. Point K is the reflection of point H across line B. Point L is the midpoint of segment HF. Line Q is the perpendicular bisector of segment HF. Let R be the rotation of point F by angle 5pi/12 around point K. Line M passes through p... | 6.5 | MATH |
[
{
"content": "ZY = 7. Point W is obtained by rotating point Y by angle 5pi/12 about point Z. Let T be the angle bisector of angle ZWY. Point L is the reflection of point Z across line T. Point S is the midpoint of segment LZ. Let R be the midpoint of segment WS. Point U is the midpoint of segment RZ. Line M pas... | 1.96 | MATH |
[
{
"content": "LZ = 8. Let F be the rotation of point L by angle pi/2 around point Z. Point X is the midpoint of segment FL. Point V is obtained by rotating point F by angle pi/3 about point Z. Let W be the perpendicular bisector of segment XL. Point R is the midpoint of segment ZF. Point D lies on line W at dis... | 7.46 | MATH |
[
{
"content": "Let RQ = 4. Let X be the rotation of point Q by angle 7pi/12 around point R. Point O is obtained by rotating point R by angle pi/4 about point Q. Point V is the reflection of point O across point X. Point F is obtained by rotating point X by angle pi/12 about point O. Let P be the rotation of poin... | 9.99 | MATH |
[
{
"content": "RG = 11. Point U is the reflection of point R across point G. Let P be the rotation of point U by angle 5pi/6 around point G. Point Q is the reflection of point P across segment GR. Let B be the midpoint of segment GQ. Point M is obtained by rotating point B by angle pi/2 about point U. Point H is... | 27.71 | MATH |
[
{
"content": "Let SI = 12. Point L is obtained by rotating point S by angle pi/12 about point I. Let B be the reflection of point S across point L. Let M be the midpoint of segment BL. Point T is the reflection of point M across segment SI. Find the length of segment TM. Express your answer as a decimal number ... | 9.32 | MATH |
[
{
"content": "DV = 1. Line H is the perpendicular bisector of segment VD. Line N passes through point V parallel to line H. Point S is on line N with |SV| = 11. Point Z lies on line H at distance 1 from point D. Point I is the reflection of point Z across point D. Point E is on line N with |ES| = 8. Let Q be th... | 2.24 | MATH |
[
{
"content": "Let AX = 3. Point F is the reflection of point A across point X. Let Z be the rotation of point X by angle pi/2 around point F. Let M be the vector from point Z to point A. Let D be point X translated by vector M. Let Y be the rotation of point D by angle 7pi/12 around point A. Let N be point Y tr... | 4.41 | MATH |
[
{
"content": "Let LI = 9. Point B is obtained by rotating point I by angle 5pi/6 about point L. Let Q be the rotation of point I by angle 2pi/3 around point B. Point V is the midpoint of segment BQ. Point R is the reflection of point V across point Q. Let F be the angle bisector of angle VQI. Line Y is the perp... | 66.76 | MATH |
[
{
"content": "Let NO = 12. Point C is the reflection of point O across point N. Let L be the midpoint of segment ON. Let D be the rotation of point C by angle 11pi/12 around point O. Let A be the reflection of point L across point O. Let V be the angle bisector of angle DLA. Point S is the reflection of point L... | 17.84 | MATH |
[
{
"content": "Let LJ = 3. Point G is obtained by rotating point J by angle 11pi/12 about point L. Let U be the reflection of point G across point J. Point X is obtained by rotating point J by angle 7pi/12 about point U. Let F be the vector from point J to point X. Let H be point L translated by vector F. Let V ... | 7.72 | MATH |
[
{
"content": "Let TP = 10. Let Q be the line through point T perpendicular to segment PT. Let M be the rotation of point T by angle pi/4 around point P. Let V be the rotation of point P by angle pi/4 around point T. Let C be the midpoint of segment PT. Point D is the reflection of point M across line Q. Let I b... | 21.32 | MATH |
[
{
"content": "Let OB = 4. Line X is the perpendicular bisector of segment OB. Line G passes through point O perpendicular to line X. Point Z lies on line X. Point R is the reflection of point Z across point O. Point D is the reflection of point R across line G. What is the distance between points D and Z? Expre... | 4.0 | MATH |
[
{
"content": "JI = 2. Line R passes through points J and I. Let P be the reflection of point I across point J. Let H be the rotation of point I by angle 11pi/12 around point J. Point Z is obtained by rotating point I by angle pi/6 about point J. Point S is obtained by rotating point H by angle pi/3 about point ... | 7.6 | MATH |
[
{
"content": "RS = 8. Let Y be the midpoint of segment SR. Let L be the rotation of point Y by angle pi/6 around point S. Point N is the reflection of point Y across point R. Point V is the midpoint of segment LN. Point Q is the reflection of point S across point L. Point Z is the midpoint of segment VQ. Find t... | 2.59 | MATH |
[
{
"content": "Let DS = 3. Let W be the rotation of point S by angle 2pi/3 around point D. Point N is the midpoint of segment DS. Let H be the angle bisector of angle WNS. Point P is the reflection of point N across point S. Point J is the reflection of point P across line H. Point R is the reflection of point S... | 7.05 | MATH |
[
{
"content": "Let WM = 11. Point Y is the midpoint of segment WM. Let P be the perpendicular bisector of segment MW. Point B is the midpoint of segment WY. Point Q is on line P. Point R is the midpoint of segment BQ. Point N is the midpoint of segment QR. Let F be the rotation of point N by angle pi/3 around po... | 2.75 | MATH |
[
{
"content": "SM = 9. Point J is the midpoint of segment SM. Line E is the perpendicular bisector of segment SM. Let D be the line through point M parallel to line E. Point V is the reflection of point J across line D. Find the distance between points J and V. Express your answer as a decimal number rounded to ... | 9.0 | MATH |
[
{
"content": "AN = 1. Let I be the rotation of point N by angle 7pi/12 around point A. Let X be the angle bisector of angle NAI. Point S is the reflection of point I across point N. Line J passes through points S and A. Let K be the rotation of point A by angle pi around point N. Line R is the reflection of lin... | 4.36 | MATH |
[
{
"content": "Let FG = 10. Line A is the perpendicular bisector of segment GF. Let P be the vector from point F to point G. Point U is the midpoint of segment GF. Let E be point U translated by vector P. Point D is the reflection of point E across line A. Line Q is the reflection of line A across point F. Point... | 118.92 | MATH |
[
{
"content": "Let OV = 6. Point L is obtained by rotating point O by angle pi/6 about point V. Let G be the reflection of point V across point O. Let T be the midpoint of segment LG. Line S is the angle bisector of angle TGL. Point J is the reflection of point V across line S. Point R is the reflection of point... | 11.93 | MATH |
[
{
"content": "YB = 10. Point M is the midpoint of segment YB. Let K be the reflection of point M across point Y. Line R is the perpendicular bisector of segment YM. Line E is the reflection of line R across point M. Point H is the reflection of point K across line E. Find the distance between points Y and H. Ex... | 20.0 | MATH |
[
{
"content": "Let GC = 12. Line E is the perpendicular bisector of segment GC. Point I is the reflection of point G across point C. Point Q is the reflection of point C across point I. Let B be the reflection of point G across point Q. Point Y is the reflection of point B across line E. Let O be the rotation of... | 55.57 | MATH |
[
{
"content": "Let VK = 1. Let G be the perpendicular bisector of segment KV. Let Z be the line through point V perpendicular to line G. Let J be the rotation of point K by angle pi/4 around point V. Point Y is the reflection of point K across point J. Line A is the angle bisector of angle YVJ. Point C is the re... | 5.76 | MATH |
[
{
"content": "Let MA = 2. Point D is the midpoint of segment MA. Let L be the rotation of point M by angle 5pi/12 around point A. Line O passes through points A and L. Let H be the rotation of point M by angle 5pi/12 around point D. Point E is the reflection of point M across line O. Point Q is the reflection o... | 1.21 | MATH |
[
{
"content": "Let DV = 12. Let K be the reflection of point V across point D. Line W is the angle bisector of angle VDK. Point E lies on line W at distance 8 from point D. Point L is the reflection of point E across segment DV. Point B is the reflection of point D across point K. Point Z is the midpoint of segm... | 22.47 | MATH |
[
{
"content": "Let VB = 2. Point Z is obtained by rotating point B by angle pi/2 about point V. Let T be the reflection of point V across point Z. Point E is the reflection of point B across point Z. Point M is obtained by rotating point E by angle pi/3 about point B. Point H is the reflection of point T across ... | 3.61 | MATH |
[
{
"content": "EM = 7. Let G be the rotation of point M by angle pi/3 around point E. Let L be the reflection of point M across point E. Point F is the midpoint of segment MG. Let I be the midpoint of segment LG. Point W is the midpoint of segment ME. Point H is the midpoint of segment GI. Point C is the reflect... | 1.05 | MATH |
[
{
"content": "NV = 8. Point Y is obtained by rotating point N by angle pi/3 about point V. Point E is the reflection of point Y across point N. Let T be the midpoint of segment EV. Let I be the midpoint of segment VN. Let B be the reflection of point N across point T. What is the length of segment BI? Express y... | 6.93 | MATH |
[
{
"content": "Let AW = 8. Point C is obtained by rotating point W by angle pi/6 about point A. Point V is the midpoint of segment WC. Let J be the reflection of point W across point C. Let M be the midpoint of segment AJ. Let G be the rotation of point W by angle 7pi/12 around point A. Line E is the perpendicul... | 3.19 | MATH |
[
{
"content": "Let GB = 8. Let N be the vector from point B to point G. Point T is the midpoint of segment GB. Point H is the reflection of point T across point G. Let L be the rotation of point B by angle pi/2 around point T. Point Q is the reflection of point G across point L. Let Y be point H translated by ve... | 3.16 | MATH |
[
{
"content": "YR = 5. Let W be the perpendicular bisector of segment RY. Let Z be the reflection of point R across point Y. Point N lies on line W at distance 9 from point Y. Point B is the reflection of point Y across point N. Let S be the midpoint of segment ZN. Line P is the perpendicular bisector of segment... | 3.85 | MATH |
[
{
"content": "LG = 8. Let T be the vector from point G to point L. Point E is the midpoint of segment GL. Let N be point E translated by vector T. Point M is on segment GL. Line R passes through point G perpendicular to segment GL. Point I is the midpoint of segment NM. Point X is the reflection of point I acro... | 16.0 | MATH |
[
{
"content": "HS = 1. Let X be the midpoint of segment SH. Let L be the rotation of point H by angle 11pi/12 around point S. Let N be the line through point S perpendicular to segment SH. Let D be the reflection of point L across point X. Let W be the midpoint of segment DS. Point J is the reflection of point L... | 0.39 | MATH |
[
{
"content": "Let MQ = 6. Point R is obtained by rotating point M by angle 7pi/12 about point Q. Let A be the angle bisector of angle QRM. Let P be the reflection of point M across point R. Let Z be the reflection of line A through point P. Let C be the midpoint of segment QR. Point X is the reflection of point... | 11.63 | MATH |
[
{
"content": "OV = 3. Let U be the rotation of point O by angle pi/3 around point V. Point H is obtained by rotating point V by angle 5pi/6 about point U. Let E be the perpendicular bisector of segment HV. Let L be the midpoint of segment VU. Point J is the reflection of point L across line E. Point Z is the mi... | 2.47 | MATH |
[
{
"content": "Let FT = 4. Let B be the rotation of point F by angle pi/6 around point T. Let X be the reflection of point B across point F. Let S be the rotation of point F by angle 3pi/4 around point X. Let R be the midpoint of segment FB. Let W be the rotation of point X by angle pi around point R. Point V is... | 19.42 | MATH |
[
{
"content": "JX = 11. Point T is the reflection of point X across point J. Line A passes through points J and X. Line Q passes through point X perpendicular to line A. Let V be the rotation of point T by angle pi/3 around point J. Point U is the reflection of point V across line Q. Let F be the reflection of p... | 16.5 | MATH |
[
{
"content": "Let HM = 11. Let F be the rotation of point H by angle pi/12 around point M. Let B be the vector from point F to point M. Point X is the translation of point M by vector B. Point U is obtained by rotating point H by angle 7pi/12 about point X. Point G is the reflection of point H across point M. L... | 62.69 | MATH |
[
{
"content": "ET = 4. Let A be the rotation of point E by angle pi/6 around point T. Point K is obtained by rotating point E by angle pi/12 about point A. Let C be the line through point E perpendicular to segment TE. Point S is the reflection of point A across line C. Let J be the reflection of point A across ... | 0.67 | MATH |
[
{
"content": "Let ZJ = 7. Let U be the rotation of point Z by angle pi/4 around point J. Line C is the perpendicular bisector of segment JZ. Point W is the reflection of point U across line C. Let L be the line through point U parallel to line C. Line D is the reflection of line C across point U. Let F be the r... | 11.1 | MATH |
[
{
"content": "WT = 9. Point L is obtained by rotating point T by angle 7pi/12 about point W. Let P be the perpendicular bisector of segment TW. Point Z is the reflection of point L across point T. Let Q be the line through point L parallel to line P. Point H is the reflection of point T across point Z. Let K be... | 50.28 | MATH |
[
{
"content": "Let RO = 8. Let W be the rotation of point O by angle 5pi/12 around point R. Let C be the vector from point R to point O. Let A be point O translated by vector C. Line E passes through points A and R. Let U be the midpoint of segment WO. Line V passes through point A parallel to segment OW. Line X... | 11.63 | MATH |
[
{
"content": "LQ = 10. Point R is the midpoint of segment QL. Let P be the rotation of point R by angle 5pi/6 around point L. Point S is the reflection of point P across point R. Point Z is the reflection of point P across point L. Line E passes through points S and P. Let V be the line through point Z parallel... | 12.39 | MATH |
[
{
"content": "UD = 6. Point B is obtained by rotating point D by angle pi/3 about point U. Point T is the midpoint of segment UD. Point J is obtained by rotating point T by angle 7pi/12 about point D. Let L be the midpoint of segment DJ. Point A is the midpoint of segment BU. Line Q passes through point D paral... | 9.44 | MATH |
[
{
"content": "KW = 7. Let C be the rotation of point W by angle 5pi/6 around point K. Point N is the midpoint of segment WK. Let V be the midpoint of segment CN. Point M is the reflection of point V across segment WK. Let E be the reflection of point M across point V. Find the length of segment EN. Express your... | 7.1 | MATH |
[
{
"content": "UK = 4. Point L is the midpoint of segment UK. Let Q be the line through point K perpendicular to segment KL. Point H is the reflection of point U across line Q. Point V is the midpoint of segment KL. What is the distance between points V and H? Express your answer as a decimal number rounded to 2... | 5.0 | MATH |
[
{
"content": "SB = 6. Point V is the midpoint of segment SB. Let W be the perpendicular bisector of segment VB. Let E be the rotation of point S by angle pi/2 around point V. Let N be the angle bisector of angle EVB. Point F is the midpoint of segment SV. Point H is on line W with |HS| = 6. Line K is the angle ... | 13.27 | MATH |
[
{
"content": "Let JN = 7. Line Y passes through point N perpendicular to segment JN. Point E is the midpoint of segment JN. Point H is the midpoint of segment EN. Let X be the reflection of point E across point J. Point P is the midpoint of segment XJ. Point C is the midpoint of segment PE. Let W be the line th... | 11.38 | MATH |
[
{
"content": "CJ = 1. Let O be the reflection of point C across point J. Point W is the reflection of point O across point C. Point F is the midpoint of segment CJ. Let L be the rotation of point O by angle 5pi/12 around point W. Let G be the midpoint of segment CF. Point Z is the reflection of point F across s... | 0.29 | MATH |
[
{
"content": "Let VS = 6. Let J be the rotation of point V by angle pi/6 around point S. Line H is the perpendicular bisector of segment SJ. Point U is the reflection of point V across line H. Let W be the rotation of point U by angle 3pi/4 around point J. Let Q be the rotation of point W by angle 7pi/12 around... | 35.72 | MATH |
[
{
"content": "QK = 4. Line I is the perpendicular bisector of segment QK. Point R is the midpoint of segment QK. Let Z be the rotation of point K by angle 5pi/6 around point Q. Let S be the reflection of point R across point Z. Point Y is the reflection of point Z across line I. Point U is the reflection of poi... | 7.06 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.