messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let ZA = 8. Let V be the rotation of point Z by angle 7pi/12 around point A. Let I be the midpoint of segment AV. Line S is the angle bisector of angle AZI. Point X is the reflection of point I across line S. Let N be the reflection of point Z across point V. Point K is the reflection of point A a... | 10.95 | MATH |
[
{
"content": "Let AB = 10. Let E be the perpendicular bisector of segment BA. Point F is obtained by rotating point A by angle pi/4 about point B. Point O lies on line E at distance 3 from point F. Let Q be the reflection of point A across point B. Point L lies on line E at distance 7 from point O. Let W be the... | 20.0 | MATH |
[
{
"content": "XZ = 10. Point D is the reflection of point X across point Z. Line E is the angle bisector of angle ZXD. Let P be the rotation of point Z by angle 2pi/3 around point X. Line L passes through point P perpendicular to line E. Point I is the reflection of point D across line L. Let U be the reflectio... | 57.66 | MATH |
[
{
"content": "Let JW = 12. Point N is obtained by rotating point J by angle pi/12 about point W. Let B be the midpoint of segment NJ. Point S is the midpoint of segment WJ. Let D be the reflection of point W across point B. Find the length of segment SD. Express your answer as a decimal number rounded to 2 deci... | 17.86 | MATH |
[
{
"content": "HK = 8. Let B be the perpendicular bisector of segment HK. Let W be the reflection of point H across point K. Point O lies on line B at distance 6 from point K. Let J be the reflection of point W across point O. Let M be the line through point O perpendicular to line B. Point R is the midpoint of ... | 1.8 | MATH |
[
{
"content": "Let TZ = 8. Point H is the midpoint of segment TZ. Point M is obtained by rotating point Z by angle 2pi/3 about point H. Let C be the reflection of point M across point H. Let G be the line through points M and Z. Point P is the reflection of point H across line G. Point B is the reflection of poi... | 10.58 | MATH |
[
{
"content": "AB = 2. Point O is obtained by rotating point A by angle pi/12 about point B. Let W be the vector from point B to point O. Let L be the angle bisector of angle BOA. Point M is the translation of point A by vector W. Let I be the line through points M and O. Let R be the reflection of line I across... | 0.19 | MATH |
[
{
"content": "EW = 11. Point G is the reflection of point W across point E. Let S be the rotation of point E by angle pi/3 around point W. Let Y be the midpoint of segment GE. Let C be the reflection of point G across point S. Let B be the vector from point E to point C. Point U is the translation of point S by... | 17.62 | MATH |
[
{
"content": "CB = 1. Line A is the perpendicular bisector of segment BC. Let Q be the line through point C perpendicular to segment BC. Point P lies on line A at distance 8 from point B. Point M is the reflection of point P across segment BC. Point J is the reflection of point P across line Q. Point O is the m... | 4.37 | MATH |
[
{
"content": "OE = 12. Let Q be the midpoint of segment EO. Point N is the reflection of point Q across point E. Point A is the reflection of point E across point N. Let X be the reflection of point A across point Q. What is the distance between points X and A? Express your answer as a decimal number rounded to... | 36.0 | MATH |
[
{
"content": "CI = 1. Point H is obtained by rotating point I by angle 2pi/3 about point C. Point U is the reflection of point H across point C. Point D is obtained by rotating point C by angle pi/6 about point I. Let R be the reflection of point C across point I. Line N passes through points R and C. Let Z be ... | 0.92 | MATH |
[
{
"content": "QE = 5. Let K be the midpoint of segment EQ. Point J is obtained by rotating point Q by angle 2pi/3 about point E. Point M is obtained by rotating point E by angle 2pi/3 about point J. Let R be the rotation of point K by angle pi/2 around point M. Let Y be the midpoint of segment KR. Point V is th... | 6.49 | MATH |
[
{
"content": "ES = 7. Point A is obtained by rotating point S by angle 5pi/12 about point E. Let X be the line through points S and A. Point Y is the reflection of point A across segment SE. Point I is the midpoint of segment SE. Line W passes through point A perpendicular to line X. Point N is the reflection o... | 14.32 | MATH |
[
{
"content": "Let HV = 8. Let T be the midpoint of segment VH. Point E is obtained by rotating point T by angle pi/6 about point V. Let M be the rotation of point T by angle pi/2 around point H. Let X be the reflection of point H across point M. Point J is the midpoint of segment EX. Point I is the reflection o... | 12.83 | MATH |
[
{
"content": "RZ = 11. Point Q is the midpoint of segment RZ. Let F be the rotation of point Q by angle 7pi/12 around point R. Point A is the reflection of point R across point Z. Let L be the reflection of point A across point Q. Let W be the reflection of point F across point R. Let U be the rotation of point... | 2.09 | MATH |
[
{
"content": "YW = 10. Point E is obtained by rotating point Y by angle 11pi/12 about point W. Let P be the midpoint of segment YE. Let K be the angle bisector of angle EPW. Point T is the reflection of point E across line K. Let Q be the line through point T perpendicular to line K. Let C be the angle bisector... | 33.17 | MATH |
[
{
"content": "OD = 7. Point H is obtained by rotating point D by angle pi/4 about point O. Point X is the reflection of point H across point D. Line M passes through points X and H. Point G is the reflection of point O across line M. Point C is the reflection of point G across point O. Find the distance between... | 19.59 | MATH |
[
{
"content": "WP = 6. Point M is the midpoint of segment WP. Point I is obtained by rotating point P by angle pi/12 about point M. Point B is the midpoint of segment IM. Let U be the reflection of point B across point M. Let X be the angle bisector of angle UMB. Point S is the midpoint of segment PU. Point R is... | 3.92 | MATH |
[
{
"content": "PU = 3. Let Z be the rotation of point U by angle pi/6 around point P. Let O be the rotation of point P by angle pi/2 around point U. Let T be the reflection of point Z across point O. Point Y is the midpoint of segment OU. Point A is the reflection of point Z across point U. Let C be the midpoint... | 3.49 | MATH |
[
{
"content": "Let LB = 12. Point O is the midpoint of segment LB. Point A is the reflection of point O across point L. Let T be the perpendicular bisector of segment AL. Let G be the line through point O parallel to line T. Let H be the rotation of point L by angle 2pi/3 around point O. Let V be the reflection ... | 40.99 | MATH |
[
{
"content": "Let VS = 10. Point C is the reflection of point S across point V. Let B be the midpoint of segment SV. Let G be the rotation of point S by angle pi/12 around point B. Point L is the reflection of point G across segment BS. Point H is the midpoint of segment CG. Line M is the perpendicular bisector... | 19.84 | MATH |
[
{
"content": "Let OW = 11. Line Y is the perpendicular bisector of segment OW. Line P passes through point W parallel to line Y. Point T is the reflection of point O across line P. Point V is the reflection of point W across point T. Line A passes through points W and T. Let U be the rotation of point V by angl... | 8.71 | MATH |
[
{
"content": "SZ = 6. Let A be the perpendicular bisector of segment SZ. Line K passes through point S parallel to line A. Point U lies on line K. Let W be the midpoint of segment SU. Let G be the reflection of point W across point Z. Point X is the reflection of point G across line K. What is the distance betw... | 24.0 | MATH |
[
{
"content": "Let NF = 1. Let H be the rotation of point F by angle 11pi/12 around point N. Let I be the midpoint of segment HN. Let D be the rotation of point I by angle 5pi/6 around point H. Let S be the midpoint of segment HD. Point G is the midpoint of segment SN. Point T is the midpoint of segment DG. Let ... | 0.82 | MATH |
[
{
"content": "Let IX = 2. Point D is the midpoint of segment IX. Let C be the rotation of point I by angle 2pi/3 around point D. Point U is obtained by rotating point X by angle 11pi/12 about point D. Let M be the midpoint of segment XC. Point S is the midpoint of segment DI. Point N is the reflection of point ... | 1.73 | MATH |
[
{
"content": "LX = 5. Let S be the midpoint of segment XL. Let T be the rotation of point L by angle 5pi/6 around point X. Line F passes through point T perpendicular to segment LX. Let P be the line through point T perpendicular to line F. Let O be the reflection of point S across point X. Point N is the refle... | 27.77 | MATH |
[
{
"content": "Let CS = 5. Let B be the perpendicular bisector of segment CS. Line N passes through point C parallel to line B. Let G be the rotation of point S by angle 11pi/12 around point C. Let K be the rotation of point G by angle pi around point S. Point M is the reflection of point C across point K. Point... | 14.97 | MATH |
[
{
"content": "Let XT = 4. Line I is the perpendicular bisector of segment XT. Let F be the rotation of point T by angle pi/6 around point X. Line K passes through point F perpendicular to line I. Point B is the reflection of point T across point X. Let P be the reflection of point F across point B. Let H be the... | 22.21 | MATH |
[
{
"content": "GV = 1. Point H is obtained by rotating point G by angle pi/2 about point V. Let W be the midpoint of segment GV. Line X is the angle bisector of angle HWV. Point D is obtained by rotating point W by angle 5pi/12 about point G. Line O passes through point H parallel to line X. Point F is the midpo... | 1.31 | MATH |
[
{
"content": "JB = 12. Let F be the reflection of point B across point J. Let G be the perpendicular bisector of segment BJ. JI = 11. Line H passes through point J perpendicular to segment BJ. Point U is the reflection of point I across line H. Let O be the reflection of point U across point B. Point P is the r... | 5.5 | MATH |
[
{
"content": "QU = 6. Let R be the rotation of point Q by angle 5pi/6 around point U. Let B be the midpoint of segment UR. Line F is the perpendicular bisector of segment QU. Point A is the reflection of point B across line F. Let C be the midpoint of segment BU. Point J is the reflection of point R across segm... | 3.97 | MATH |
[
{
"content": "Let AC = 3. Point F is the reflection of point C across point A. Let K be the midpoint of segment AC. Point N is obtained by rotating point F by angle 5pi/12 about point K. Let Z be the rotation of point F by angle pi/12 around point C. Line D passes through points Z and N. Let W be the reflection... | 19.46 | MATH |
[
{
"content": "ZI = 6. ZD = 12. Let L be the midpoint of segment DZ. Let O be the vector from point L to point D. Point H is obtained by rotating point D by angle pi/6 about point L. Point B is the translation of point I by vector O. Let W be the line through points Z and B. Line A passes through point H paralle... | 3.11 | MATH |
[
{
"content": "Let FJ = 10. Let O be the rotation of point F by angle 5pi/12 around point J. Let Z be the midpoint of segment JO. Let R be the midpoint of segment JZ. Let Y be the midpoint of segment RF. What is the distance between points Y and Z? Express your answer as a decimal number rounded to 2 decimal pla... | 5.42 | MATH |
[
{
"content": "Let YR = 2. Let W be the midpoint of segment YR. Point L is obtained by rotating point W by angle pi/12 about point R. Line X is the perpendicular bisector of segment WL. Line K is the reflection of line X across point Y. Let H be the rotation of point W by angle 5pi/6 around point Y. Let F be the... | 2.24 | MATH |
[
{
"content": "IQ = 12. Let F be the rotation of point Q by angle 5pi/12 around point I. Point R is the midpoint of segment IQ. Point L is obtained by rotating point Q by angle 2pi/3 about point R. Line T is the angle bisector of angle QRL. Let J be the reflection of point Q across point I. Point O is the reflec... | 3.11 | MATH |
[
{
"content": "Let ZP = 3. Point H is the reflection of point Z across point P. Line N is the perpendicular bisector of segment ZH. Point T lies on line N at distance 9 from point H. Let G be the reflection of point T across point P. Let E be the reflection of point G across point T. Let B be the midpoint of seg... | 22.55 | MATH |
[
{
"content": "BU = 12. Line D is the perpendicular bisector of segment UB. Let G be the midpoint of segment UB. Let I be the midpoint of segment GB. Line T is the perpendicular bisector of segment GB. Point M is the midpoint of segment UI. Let V be the line through point B parallel to line T. Let Q be the rotat... | 2.81 | MATH |
[
{
"content": "UK = 5. Point E is on segment UK. Point C is the midpoint of segment EK. T is constructed so that KT = 3. Let V be the midpoint of segment CK. Let Q be the reflection of point T across point V. Point Z is the reflection of point C across segment TQ. Find the length of segment QZ. Express your answ... | 3.0 | MATH |
[
{
"content": "RD = 9. Let K be the reflection of point D across point R. Point W is obtained by rotating point D by angle 3pi/4 about point K. Line P passes through points W and D. Line H is the perpendicular bisector of segment KW. Point M is the reflection of point K across point D. Let A be the line through ... | 76.57 | MATH |
[
{
"content": "Let IF = 9. Point H is obtained by rotating point F by angle 5pi/6 about point I. Let R be the rotation of point F by angle pi around point I. Let G be the midpoint of segment IH. Let B be the reflection of point G across point R. Point Q is obtained by rotating point H by angle pi/4 about point R... | 16.09 | MATH |
[
{
"content": "NV = 8. Let D be the perpendicular bisector of segment VN. Let U be the vector from point V to point N. Let X be the rotation of point V by angle 5pi/12 around point N. Line B passes through points N and X. Point J is the translation of point N by vector U. Point Y is the reflection of point J acr... | 22.63 | MATH |
[
{
"content": "RB = 1. Let T be the rotation of point R by angle 7pi/12 around point B. Line A is the angle bisector of angle RBT. Point G is obtained by rotating point R by angle 11pi/12 about point T. Point L is the reflection of point R across point G. Point K is the reflection of point G across line A. Let Y... | 15.32 | MATH |
[
{
"content": "Let CP = 12. Point E is obtained by rotating point C by angle pi/4 about point P. Let N be the rotation of point E by angle 11pi/12 around point P. Line G is the angle bisector of angle NEC. Point X is the reflection of point P across line G. Let M be the reflection of point X across point E. Poin... | 10.04 | MATH |
[
{
"content": "KL = 3. Line Q passes through points L and K. Let J be the rotation of point L by angle 11pi/12 around point K. Point D is the reflection of point J across point L. Line W is the angle bisector of angle KDJ. Line P is the reflection of line Q across line W. Point V is obtained by rotating point J ... | 4.97 | MATH |
[
{
"content": "TX = 7. Let U be the vector from point T to point X. Let O be point X translated by vector U. Let V be the reflection of point O across point T. Point Y is obtained by rotating point O by angle pi/4 about point X. Let C be point O translated by vector U. Point M is the reflection of point V across... | 2.58 | MATH |
[
{
"content": "Let MV = 1. Let Y be the reflection of point M across point V. Point L is the reflection of point V across point Y. Point X is the reflection of point V across point M. Line F is the perpendicular bisector of segment VL. Let W be the midpoint of segment YX. Point I is on line F with |IM| = 5. Poin... | 11.38 | MATH |
[
{
"content": "PR = 12. Let F be the vector from point R to point P. Let O be the reflection of point P across point R. Point B is obtained by rotating point P by angle pi/12 about point O. Point X is the translation of point P by vector F. Let Z be the rotation of point B by angle 7pi/12 around point P. Point E... | 8.95 | MATH |
[
{
"content": "Let WJ = 12. Let D be the rotation of point W by angle pi around point J. Line S is the angle bisector of angle DWJ. Line U passes through point J perpendicular to line S. Point M is on line U with |MJ| = 11. Let C be the perpendicular bisector of segment MD. Line I is the reflection of line C acr... | 13.46 | MATH |
[
{
"content": "QA = 6. Let N be the reflection of point A across point Q. Let C be the angle bisector of angle NQA. Let O be the line through point A parallel to line C. Line H is the reflection of line O across line C. Point U is the reflection of point A across line H. Point V is the reflection of point U acro... | 12.53 | MATH |
[
{
"content": "Let SE = 8. Point V is the midpoint of segment ES. Let D be the reflection of point V across point S. Point U is the midpoint of segment SV. Let Q be the perpendicular bisector of segment US. Point J is obtained by rotating point U by angle 11pi/12 about point V. Point C is the reflection of point... | 1.19 | MATH |
[
{
"content": "CD = 10. Let L be the rotation of point C by angle pi/4 around point D. Let W be the midpoint of segment DC. Let V be the reflection of point D across point L. Point I is the midpoint of segment LD. Let K be the reflection of point V across point I. Point T is the reflection of point W across poin... | 18.87 | MATH |
[
{
"content": "Let XO = 6. Point S is obtained by rotating point O by angle 7pi/12 about point X. Line Y is the perpendicular bisector of segment XS. Let V be the perpendicular bisector of segment SO. Let F be the rotation of point O by angle 3pi/4 around point S. Let A be the reflection of line V through point ... | 33.62 | MATH |
[
{
"content": "PA = 7. Point I is the midpoint of segment AP. Point B is the reflection of point A across point P. Point N is the midpoint of segment IA. Let T be the midpoint of segment IB. Line D is the perpendicular bisector of segment NB. Point G is on line D with |GI| = 9. Let U be the angle bisector of ang... | 8.13 | MATH |
[
{
"content": "Let QX = 11. Point B is the midpoint of segment QX. Let F be the reflection of point B across point Q. Point Y is obtained by rotating point X by angle pi/12 about point B. Point G is the midpoint of segment YB. Let C be the rotation of point Y by angle 11pi/12 around point F. Point A is obtained ... | 62.61 | MATH |
[
{
"content": "RT = 1. Let C be the rotation of point T by angle 11pi/12 around point R. Let L be the rotation of point C by angle 11pi/12 around point R. Point V is the reflection of point L across point C. Line O is the angle bisector of angle VTL. Let Y be the line through point L perpendicular to line O. Let... | 5.9 | MATH |
[
{
"content": "Let ZQ = 8. B is placed 7 units away from Q. Let C be the vector from point Q to point Z. Let I be the rotation of point B by angle pi around point Q. Point S is the translation of point I by vector C. Let H be the rotation of point Z by angle pi/3 around point Q. Point G is the reflection of poin... | 22.42 | MATH |
[
{
"content": "WA = 9. Line O is the perpendicular bisector of segment AW. Line D passes through point W parallel to line O. Point B is the reflection of point A across line D. Let X be the reflection of point B across point A. Let K be the reflection of point X across point B. Let U be the rotation of point A b... | 27.19 | MATH |
[
{
"content": "Let FW = 6. Line G is the perpendicular bisector of segment WF. Line D is the reflection of line G across point W. Point T is on line G. Let C be the reflection of point F across point T. Point K is on line D with |KT| = 2. Point Q is the reflection of point K across line G. Let M be the reflectio... | 14.42 | MATH |
[
{
"content": "NV = 8. W is placed 4 units away from V. Let NR = 8. Point A is the midpoint of segment RW. Point B is the midpoint of segment WN. Let G be the midpoint of segment AB. Let O be the midpoint of segment AG. What is the length of segment BO? Express your answer as a decimal number rounded to 2 decima... | 3.0 | MATH |
[
{
"content": "Let SA = 2. Let F be the rotation of point A by angle 11pi/12 around point S. Let O be the midpoint of segment FA. Point V is the reflection of point S across point A. Point X is the reflection of point O across segment AS. Point B is the midpoint of segment XO. Find the distance between points B ... | 3.97 | MATH |
[
{
"content": "SO = 3. Let J be the midpoint of segment OS. Point Q is the midpoint of segment JS. Point L is obtained by rotating point O by angle pi/12 about point Q. Point K is obtained by rotating point J by angle 5pi/12 about point Q. Point T is the midpoint of segment OK. Let M be the angle bisector of ang... | 1.09 | MATH |
[
{
"content": "AM = 10. Point P is the reflection of point A across point M. Point X is the midpoint of segment AM. Let H be the midpoint of segment PM. Let W be the rotation of point H by angle pi around point A. Let V be the rotation of point X by angle 3pi/4 around point H. Let T be the angle bisector of angl... | 62.56 | MATH |
[
{
"content": "Let TE = 3. Let H be the midpoint of segment TE. Let G be the vector from point T to point E. Point N is obtained by rotating point E by angle 2pi/3 about point H. Let L be the line through points E and H. Point A is the reflection of point E across point N. Point D is the midpoint of segment HT. ... | 6.92 | MATH |
[
{
"content": "DA = 8. Let V be the reflection of point A across point D. Let Y be the reflection of point D across point V. Let O be the rotation of point D by angle pi/6 around point V. Let F be the perpendicular bisector of segment VO. Let E be the midpoint of segment OV. Point U is the reflection of point V ... | 1.65 | MATH |
[
{
"content": "Let CX = 2. Point P is the midpoint of segment XC. Let M be the midpoint of segment PX. Let D be the angle bisector of angle CPM. Let J be the midpoint of segment CP. Line I is the reflection of line D across point C. Line H is the reflection of line I across point J. Point T is the reflection of ... | 4.0 | MATH |
[
{
"content": "Let LV = 7. Point H is the reflection of point V across point L. Let F be the midpoint of segment LV. Point T is the midpoint of segment LH. Point R is obtained by rotating point T by angle 5pi/12 about point L. Point C is the midpoint of segment LR. Let Z be the rotation of point L by angle 3pi/4... | 8.2 | MATH |
[
{
"content": "CF = 1. Let R be the rotation of point C by angle 2pi/3 around point F. Line Y is the angle bisector of angle CFR. Let I be the reflection of line Y through point C. Point N is the midpoint of segment FR. Let S be the midpoint of segment CN. Point H is the reflection of point N across line I. Find... | 3.68 | MATH |
[
{
"content": "Let OP = 2. Point M is the reflection of point P across point O. Let B be the reflection of point M across point P. Line S is the perpendicular bisector of segment PM. Line A passes through point M parallel to line S. Let Q be the reflection of point O across point P. Let C be the reflection of li... | 29.0 | MATH |
[
{
"content": "Let WJ = 11. Let N be the midpoint of segment WJ. Point S is obtained by rotating point J by angle pi/6 about point W. Point P is the midpoint of segment NW. Let L be the reflection of point S across point P. Let I be the reflection of point L across point W. Find the measure of angle ISJ, in radi... | 1.83 | MATH |
[
{
"content": "OG = 2. Point E is the midpoint of segment GO. Point N is obtained by rotating point O by angle 7pi/12 about point E. Let A be the perpendicular bisector of segment EN. Let B be the line through point O parallel to line A. Line H passes through point E perpendicular to line B. Let V be the rotatio... | 0.27 | MATH |
[
{
"content": "Let XJ = 5. Point Z is obtained by rotating point J by angle pi/3 about point X. Let B be the rotation of point J by angle 3pi/4 around point X. Point A is the reflection of point Z across point B. Point D is the midpoint of segment JB. Let Y be the perpendicular bisector of segment XZ. Point H is... | 10.91 | MATH |
[
{
"content": "TF = 11. Let X be the reflection of point F across point T. Point M is obtained by rotating point F by angle 5pi/6 about point T. Line W is the angle bisector of angle FMX. Point B is the reflection of point X across line W. Let S be the reflection of point T across point M. Let R be the reflectio... | 8.28 | MATH |
[
{
"content": "Let FS = 8. Let X be the rotation of point F by angle pi/12 around point S. Point A is the midpoint of segment SX. Let Y be the line through points F and S. Let FE = 2. Line G is the reflection of line Y across point E. Point K is the reflection of point X across line G. Line Q is the angle bisect... | 0.55 | MATH |
[
{
"content": "Let KF = 2. Let N be the midpoint of segment KF. Z is placed 11 units away from N. Line I is the perpendicular bisector of segment ZN. Point E is on line I. Point X is the reflection of point E across segment FZ. Let U be the line through points X and K. Point A is the reflection of point N across... | 1.0 | MATH |
[
{
"content": "HZ = 9. Let Q be the line through points Z and H. Point P lies on line Q. Point Y is the reflection of point Z across point H. Line F passes through point Z perpendicular to line Q. Let X be the midpoint of segment ZP. Point G is the reflection of point Y across line F. Line B is the perpendicular... | 18.0 | MATH |
[
{
"content": "Let VF = 10. Let H be the perpendicular bisector of segment VF. Let B be the rotation of point F by angle pi/4 around point V. Line A passes through points B and F. Line I passes through point V parallel to line A. Line P is the reflection of line H across point B. Let Y be the reflection of line ... | 17.93 | MATH |
[
{
"content": "Let IT = 9. Point X is the midpoint of segment TI. Point H is obtained by rotating point I by angle pi/4 about point T. Let W be the reflection of point H across point X. Line S is the perpendicular bisector of segment TI. Point E is the reflection of point W across line S. Line D is the reflectio... | 7.51 | MATH |
[
{
"content": "Let WB = 5. Let G be the reflection of point W across point B. Line I is the perpendicular bisector of segment WG. Point V lies on line I at distance 9 from point W. Let H be the midpoint of segment VB. Point O is the midpoint of segment HB. Point T is the midpoint of segment HG. Point A is the re... | 2.5 | MATH |
[
{
"content": "Let IJ = 7. Point H is obtained by rotating point I by angle pi/6 about point J. Line L is the perpendicular bisector of segment JI. Line T is the angle bisector of angle HJI. Let V be the line through point H parallel to line T. Let B be the reflection of line V across line T. Line P is the refle... | 9.66 | MATH |
[
{
"content": "Let OH = 10. Let I be the midpoint of segment HO. Let C be the rotation of point I by angle 2pi/3 around point H. Point K is the midpoint of segment IC. Let U be the line through points C and H. Let F be the line through point C perpendicular to line U. Point Y is the reflection of point H across ... | 9.01 | MATH |
[
{
"content": "Let GB = 11. Let C be the line through points B and G. Let F be the rotation of point B by angle pi/3 around point G. Point I lies on line C. V is placed 10 units away from I. Let U be the perpendicular bisector of segment GI. Let J be the midpoint of segment FB. Point Q is the midpoint of segment... | 4.96 | MATH |
[
{
"content": "AL = 8. Let J be the midpoint of segment LA. Point P is the reflection of point J across point A. Point S is obtained by rotating point A by angle 3pi/4 about point P. Let W be the midpoint of segment LS. Line V is the perpendicular bisector of segment AP. Point N is the reflection of point L acro... | 16.65 | MATH |
[
{
"content": "UH = 9. Let A be the perpendicular bisector of segment UH. Line T passes through point H parallel to line A. Point P lies on line T. Let M be the midpoint of segment HP. Point C is the midpoint of segment UP. What is the distance between points M and C? Express your answer as a decimal number roun... | 4.5 | MATH |
[
{
"content": "Let GT = 8. Point U is obtained by rotating point T by angle 5pi/12 about point G. Point M is the midpoint of segment TG. Let W be the line through points U and G. Let J be the reflection of line W through point T. Point X is the reflection of point T across point U. Point Y is the reflection of p... | 7.73 | MATH |
[
{
"content": "Let GW = 8. Point A is obtained by rotating point W by angle pi/6 about point G. Let S be the midpoint of segment AW. Point P is the midpoint of segment AS. Line V passes through point P perpendicular to segment WG. Point E is the reflection of point G across line V. Point O is the reflection of p... | 8.47 | MATH |
[
{
"content": "Let YJ = 12. Point A is obtained by rotating point J by angle 5pi/12 about point Y. Point Q is obtained by rotating point Y by angle pi/3 about point J. Let C be the vector from point J to point Y. Let U be the rotation of point Q by angle 7pi/12 around point Y. Let M be the perpendicular bisector... | 8.64 | MATH |
[
{
"content": "GW = 9. Let H be the rotation of point G by angle pi/4 around point W. Point L is the midpoint of segment WG. Point C is the midpoint of segment HL. Point J is the reflection of point C across segment GW. What is the distance between points L and J? Express your answer as a decimal number rounded ... | 3.32 | MATH |
[
{
"content": "YM = 1. Let L be the reflection of point M across point Y. Line G is the perpendicular bisector of segment LM. Let W be the midpoint of segment YL. Line O is the reflection of line G across point W. Point Z is the reflection of point Y across line O. Find the distance between points Z and Y. Expre... | 2.0 | MATH |
[
{
"content": "SP = 7. Let M be the rotation of point P by angle pi/12 around point S. Point D is obtained by rotating point M by angle pi/6 about point P. Let J be the perpendicular bisector of segment PS. Point F is obtained by rotating point M by angle pi about point S. Let C be the line through points F and ... | 9.04 | MATH |
[
{
"content": "AN = 4. Let W be the vector from point A to point N. Let K be the midpoint of segment NA. Let H be point K translated by vector W. Point B is obtained by rotating point K by angle 5pi/12 about point N. Let I be the midpoint of segment NK. Let Z be the line through point A perpendicular to segment ... | 9.96 | MATH |
[
{
"content": "Let EA = 11. Point O is obtained by rotating point A by angle 5pi/12 about point E. Point C is the reflection of point E across point O. Let H be the reflection of point O across point C. Let N be the perpendicular bisector of segment AE. Point U is the reflection of point E across point H. Line I... | 22.78 | MATH |
[
{
"content": "Let YB = 11. Point D is obtained by rotating point B by angle 7pi/12 about point Y. Let N be the perpendicular bisector of segment YB. Let J be the reflection of line N through point D. Let H be the reflection of line J through point Y. Point R is the reflection of point D across line H. Point G i... | 17.08 | MATH |
[
{
"content": "MZ = 6. Point Q is the midpoint of segment MZ. Let G be the vector from point Z to point Q. Let N be the perpendicular bisector of segment ZQ. Let L be the line through points Z and Q. Point C is obtained by rotating point Q by angle pi/4 about point M. Let A be the perpendicular bisector of segme... | 18.14 | MATH |
[
{
"content": "DR = 6. Let C be the reflection of point R across point D. Let I be the line through points C and R. Line B passes through point D perpendicular to line I. Let M be the rotation of point D by angle 2pi/3 around point C. Let W be the line through point C perpendicular to line I. Point O is the refl... | 4.42 | MATH |
[
{
"content": "PU = 6. Point A is obtained by rotating point P by angle pi/6 about point U. Point V is the reflection of point P across point U. Point Y is obtained by rotating point V by angle pi/12 about point P. Point Z is the reflection of point V across point P. Let M be the reflection of point V across poi... | 44.29 | MATH |
[
{
"content": "DW = 2. Let E be the midpoint of segment WD. Point K is the midpoint of segment EW. Let M be the rotation of point W by angle 3pi/4 around point D. Point H is the reflection of point K across point E. Let V be the reflection of point M across point D. Point T is the midpoint of segment VK. What is... | 1.19 | MATH |
[
{
"content": "Let MO = 10. Line S is the perpendicular bisector of segment OM. Let N be the rotation of point O by angle 3pi/4 around point M. Let T be the midpoint of segment MN. Point U is obtained by rotating point N by angle 5pi/12 about point T. Let R be the midpoint of segment UM. Point P is the midpoint ... | 17.06 | MATH |
[
{
"content": "Let AG = 4. Point H is the midpoint of segment GA. Let R be the vector from point G to point A. Let F be point A translated by vector R. Point N is obtained by rotating point F by angle pi/4 about point H. Point Q is the translation of point F by vector R. Line O is the perpendicular bisector of s... | 13.46 | MATH |
[
{
"content": "QA = 5. Point M is the reflection of point Q across point A. Line B passes through point Q perpendicular to segment QA. Line D is the reflection of line B across point M. Line X is the reflection of line D across line B. Let V be the perpendicular bisector of segment QA. Point I lies on line V. Po... | 45.0 | MATH |
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