messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let JU = 7. Let C be the rotation of point U by angle pi/2 around point J. Let T be the rotation of point J by angle pi/12 around point U. Let L be the midpoint of segment UT. Point V is the reflection of point L across segment TC. Let O be the centroid of triangle TCU. What is the distance betwee... | 6.27 | MATH |
[
{
"content": "GO = 5. Line J is the perpendicular bisector of segment OG. Let Z be the line through point O parallel to line J. Let P be the reflection of line J across line Z. Point C is obtained by rotating point O by angle pi/3 about point G. Let Q be the rotation of point O by angle 5pi/12 around point G. L... | 25.09 | MATH |
[
{
"content": "Let PV = 4. Let Z be the rotation of point P by angle pi/12 around point V. Line J is the perpendicular bisector of segment ZV. Let B be the line through point Z parallel to line J. Line G passes through point V parallel to line B. Point C is the reflection of point P across line G. Let R be the o... | 1.93 | MATH |
[
{
"content": "Let CX = 3. Point J is obtained by rotating point C by angle pi/2 about point X. Point H is the midpoint of segment XC. Point A is obtained by rotating point H by angle 5pi/6 about point C. Let F be the midpoint of segment XJ. Let G be the reflection of point F across point A. Let Z be the circumc... | 17.98 | MATH |
[
{
"content": "Let YA = 4. Point E is obtained by rotating point A by angle pi/6 about point Y. Let V be the rotation of point Y by angle 5pi/12 around point E. Let G be the rotation of point V by angle pi/12 around point Y. Let I be the midpoint of segment YG. Let N be the circumcenter of triangle YIV. Point R ... | 2.42 | MATH |
[
{
"content": "Let TC = 5. Point V is obtained by rotating point T by angle pi/3 about point C. Point K is the midpoint of segment CV. Let H be the circumcenter of triangle KTV. Let B be the midpoint of segment HV. What is the distance between points B and V? Express your answer as a decimal number rounded to 2 ... | 1.1 | MATH |
[
{
"content": "FJ = 8. Let K be the reflection of point F across point J. Point O is obtained by rotating point F by angle pi/4 about point K. Let W be the midpoint of segment JK. Let Y be the midpoint of segment WK. Point E is obtained by rotating point F by angle pi/3 about point K. Point A is the reflection o... | 50.16 | MATH |
[
{
"content": "UM = 2. Let H be the perpendicular bisector of segment MU. Point N is obtained by rotating point U by angle 5pi/12 about point M. Point O is the reflection of point N across line H. Point W is the incenter of triangle MNO. Let J be the circumcenter of triangle MNO. Find the measure of angle WOJ, i... | 0.08 | MATH |
[
{
"content": "Let OH = 8. Let U be the perpendicular bisector of segment OH. Point G is on line U with |GH| = 3. Let W be the reflection of point O across point G. Let C be the orthocenter of triangle HGO. Let N be the reflection of point H across point C. Find the measure of angle NCW, in radians. Express your... | 12.0 | MATH |
[
{
"content": "Point E is the reflection of point B across segment YY40. Point V is obtained by rotating point B by angle pi about point E. Let Q be the angle bisector of angle DBE. Circle J is the circumcircle of triangle D. Circle X is the reflection of circle J across line Q. Point C is the inversion of point... | 1.92 | MATH |
[
{
"content": "SC = 12. Point A is obtained by rotating point C by angle 2pi/3 about point S. Point P is the centroid of triangle ASC. Line B passes through point S perpendicular to segment SC. Point G is the reflection of point P across line B. Find the distance between points P and G. Express your answer as a ... | 4.0 | MATH |
[
{
"content": "Let BH = 9. Line J is the perpendicular bisector of segment HB. Let O be the line through point B perpendicular to line J. Point A is the midpoint of segment HB. Let X be the midpoint of segment HA. Let I be the rotation of point A by angle pi/6 around point X. Point U is obtained by rotating poin... | 5.31 | MATH |
[
{
"content": "DB = 6. Let S be the rotation of point B by angle 3pi/4 around point D. Point W is the reflection of point S across point D. Let H be the reflection of point W across point S. Let C be the centroid of triangle SBD. What is the distance between points H and C? Express your answer as a decimal numbe... | 17.47 | MATH |
[
{
"content": "JH = 12. JA = 1. Let D be the rotation of point A by angle 3pi/4 around point H. Point O lies on segment HA. Let L be the line through point O parallel to segment DH. Let W be the incenter of triangle ADH. Let Z be the line through point W parallel to line L. Segment HA and line Z intersect at poi... | 2.36 | MATH |
[
{
"content": "LQ = 8. Let H be the vector from point Q to point L. Point E is the translation of point L by vector H. Let I be the line through points E and Q. Line O passes through point E perpendicular to line I. Point V is on line O with |VQ| = 10. Let U be the perpendicular bisector of segment QV. Point Y i... | 207.64 | MATH |
[
{
"content": "Let QL = 11. Point M is obtained by rotating point L by angle pi/2 about point Q. Let C be the rotation of point Q by angle pi/6 around point M. Point K is obtained by rotating point M by angle 5pi/12 about point L. Let R be the incircle of triangle QKM. Point G is the midpoint of segment MQ. Let ... | 4.49 | MATH |
[
{
"content": "GB = 7. Point I is obtained by rotating point G by angle 2pi/3 about point B. Let U be the rotation of point B by angle pi/2 around point G. Let C be the midpoint of segment GU. Point L is the incenter of triangle GUI. Line K passes through points L and G. Point E is the intersection of segment UI... | 4.05 | MATH |
[
{
"content": "Let HN = 6. Point S is the midpoint of segment NH. Point P is the midpoint of segment SN. Point A is the reflection of point S across point N. Point L is the midpoint of segment AN. Point W is obtained by rotating point H by angle 2pi/3 about point S. Let V be the reflection of point S across poin... | 14.47 | MATH |
[
{
"content": "OE = 9. Let A be the perpendicular bisector of segment OE. Let Q be the reflection of line A through point O. Let R be the rotation of point E by angle 11pi/12 around point O. Let T be the reflection of line Q across line A. Let Y be the rotation of point R by angle pi/6 around point E. Point P is... | 6263.89 | MATH |
[
{
"content": "FE = 1. Point A is obtained by rotating point E by angle pi/2 about point F. Point I is obtained by rotating point A by angle pi/6 about point F. Line V is the angle bisector of angle FAI. Point M is the midpoint of segment EF. Let L be the perpendicular bisector of segment FI. Let G be the circum... | 2.41 | MATH |
[
{
"content": "Let FR = 6. Let Y be the rotation of point F by angle 2pi/3 around point R. Let W be the reflection of point F across point R. Point C is the reflection of point F across segment RY. Let V be the centroid of triangle RYF. What is the circumradius of triangle VCW? Express your answer as a decimal n... | 4.16 | MATH |
[
{
"content": "Let VU = 9. Point J is the midpoint of segment VU. Point O is the reflection of point V across point U. Let D be the rotation of point V by angle pi/6 around point J. Let A be the perpendicular bisector of segment OJ. Point X is the reflection of point V across segment OD. Point T is the reflectio... | 0.37 | MATH |
[
{
"content": "Let LW = 9. Point D is obtained by rotating point W by angle 5pi/12 about point L. Let R be the angle bisector of angle DLW. Let K be the line through point W parallel to line R. Point Z is the reflection of point L across line K. Let G be the orthocenter of triangle LDW. What is the measure of an... | 0.26 | MATH |
[
{
"content": "YK = 10. Line C is the perpendicular bisector of segment YK. Point G lies on line C at distance 12 from point K. Point J is the midpoint of segment KG. Let T be the midpoint of segment JY. Circle B is the circumcircle of triangle GJY. Point A is the midpoint of segment YT. Let F be the inversion o... | 7.84 | MATH |
[
{
"content": "Let AI = 6. Point J is the reflection of point I across point A. Let B be the line through points A and J. Point D is obtained by rotating point I by angle pi/3 about point J. Point T is the reflection of point D across point I. Line R is the reflection of line B across point T. Line K is the refl... | 374.12 | MATH |
[
{
"content": "LH = 6. Line R is the perpendicular bisector of segment LH. Let Y be the vector from point H to point L. Point X is the reflection of point L across point H. Point G is on line R with |GX| = 8. Line S passes through points X and L. Let M be point G translated by vector Y. Point D lies on line S at... | 6.0 | MATH |
[
{
"content": "XJ = 5. Point K is obtained by rotating point J by angle 3pi/4 about point X. Line A is the angle bisector of angle XKJ. Point N is on line A. Point R is the reflection of point K across segment XN. Find the length of segment RX. Express your answer as a decimal number rounded to 2 decimal places.... | 5.0 | MATH |
[
{
"content": "Let UO = 1. Point B is obtained by rotating point U by angle pi/6 about point O. Let K be the reflection of point B across point U. Let F be the orthocenter of triangle OBK. Let G be the midpoint of segment OF. Let P be the incenter of triangle OBK. Find the distance between points G and P. Expres... | 0.31 | MATH |
[
{
"content": "FY = 5. Point S is obtained by rotating point F by angle pi/6 about point Y. Point A is obtained by rotating point Y by angle 3pi/4 about point S. Let M be the midpoint of segment FA. Point Q is the midpoint of segment AS. Point N is the midpoint of segment MQ. Find the length of segment NS. Expre... | 2.88 | MATH |
[
{
"content": "WT = 3. Point X is obtained by rotating point T by angle pi/4 about point W. Let K be the incenter of triangle WTX. Line V passes through points K and W. Point M is the intersection of segment TX and line V. Find the distance between points M and W. Express your answer as a decimal number rounded ... | 2.77 | MATH |
[
{
"content": "Let AS = 2. Let W be the midpoint of segment SA. Let H be the line through points W and A. Let R be the line through point A perpendicular to line H. Line G passes through point W parallel to line R. Point V is on line G with |VS| = 4. Point T is the midpoint of segment VS. Let C be the reflection... | 5.5 | MATH |
[
{
"content": "Let LP = 11. Let M be the rotation of point L by angle 7pi/12 around point P. Point B is the midpoint of segment ML. Let F be the rotation of point B by angle pi/2 around point L. Point Q is the incenter of triangle LMF. Point T is the midpoint of segment FL. Let I be the centroid of triangle LMF.... | 0.57 | MATH |
[
{
"content": "Let FZ = 11. Let R be the midpoint of segment FZ. Point W is obtained by rotating point R by angle 5pi/6 about point Z. Let H be the midpoint of segment RW. Let K be the rotation of point F by angle pi/4 around point W. Line Y is the angle bisector of angle ZKF. Point E is the reflection of point ... | 5.08 | MATH |
[
{
"content": "Let LU = 6. Let O be the rotation of point U by angle 7pi/12 around point L. Let P be the orthocenter of triangle LOU. Let Y be the reflection of point L across point P. Point J is the reflection of point Y across segment LO. Find the distance between points J and L. Express your answer as a decim... | 5.1 | MATH |
[
{
"content": "QR = 10. Let N be the reflection of point R across point Q. Let D be the rotation of point Q by angle pi/4 around point R. Point O is the reflection of point D across point N. Point X is the midpoint of segment QN. Let G be the midpoint of segment XD. What is the distance between points G and O? E... | 24.33 | MATH |
[
{
"content": "DN = 5. Let W be the reflection of point D across point N. Let G be the angle bisector of angle DNW. Point F lies on line G at distance 3 from point D. Let K be the incenter of triangle WFD. Point T is the midpoint of segment WF. Point M is the midpoint of segment TK. What is the length of segment... | 1.25 | MATH |
[
{
"content": "Let QK = 7. Point S is the midpoint of segment KQ. Let L be the perpendicular bisector of segment SQ. Let F be the reflection of point S across point Q. I is constructed so that SI = 12. Point P lies on line L. Let N be the reflection of point S across point I. Let X be the midpoint of segment KP.... | 5.25 | MATH |
[
{
"content": "Let KZ = 7. Let V be the rotation of point Z by angle 5pi/12 around point K. Let X be the rotation of point K by angle 11pi/12 around point Z. Point N is the reflection of point V across segment KZ. Line T passes through point Z perpendicular to segment KZ. Point O is the reflection of point X acr... | 4.27 | MATH |
[
{
"content": "Let SC = 10. Point F is obtained by rotating point C by angle 2pi/3 about point S. Line V is the angle bisector of angle FCS. Line Z is the reflection of line V across point F. Point P is the reflection of point F across point C. Let Q be the orthocenter of triangle PSF. Point U is the reflection ... | 54.77 | MATH |
[
{
"content": "Let NW = 8. Let K be the midpoint of segment NW. Let M be the perpendicular bisector of segment KN. Point Y lies on line M at distance 2 from point W. Point E is the midpoint of segment KY. Let A be the orthocenter of triangle WKY. Find the inradius of triangle EWA. Express your answer as a decima... | 1.74 | MATH |
[
{
"content": "RQ = 10. Point D is obtained by rotating point R by angle 5pi/6 about point Q. Let L be the incenter of triangle DRQ. Let F be the circumcircle of triangle DRQ. Point X is the circumcenter of triangle DRQ. Point U is the circumcenter of triangle RLX. Let Y be the inversion of point U in circle F. ... | 4.92 | MATH |
[
{
"content": "Let AG = 10. Line F passes through points A and G. Point N is obtained by rotating point G by angle pi/3 about point A. Let W be the midpoint of segment NG. Let D be the midpoint of segment WA. Point L is the reflection of point W across line F. Let T be the circumcenter of triangle LDN. Point H i... | 2.2 | MATH |
[
{
"content": "Let IP = 12. Let R be the midpoint of segment PI. Point A is obtained by rotating point P by angle 11pi/12 about point I. Point U is the midpoint of segment AI. Let M be the circumcenter of triangle RAI. Point H lies on segment AI. Let N be the angle bisector of angle HIM. Point G is the reflectio... | 4.37 | MATH |
[
{
"content": "Let HB = 2. Let Y be the rotation of point B by angle pi/12 around point H. Line V is the perpendicular bisector of segment HB. Line C passes through point Y perpendicular to segment HB. Point W is obtained by rotating point Y by angle 5pi/12 about point B. Point O is obtained by rotating point W ... | 3.38 | MATH |
[
{
"content": "Let SI = 8. E is constructed so that IE = 1. Let Z be the midpoint of segment SE. Point F is the reflection of point Z across point I. Line J passes through point I perpendicular to segment EI. Let Y be the midpoint of segment EI. Point L is the reflection of point Y across line J. What is the dis... | 4.0 | MATH |
[
{
"content": "US = 2. Point B is obtained by rotating point U by angle 5pi/12 about point S. Point N is the midpoint of segment BS. Let Q be the midpoint of segment UN. Let P be the orthocenter of triangle SUN. Point W is the centroid of triangle SUN. Find the measure of angle QWP, in radians. Express your answ... | 0.07 | MATH |
[
{
"content": "WQ = 1. Point L is obtained by rotating point Q by angle pi about point W. Let Y be the perpendicular bisector of segment WL. Point J is obtained by rotating point W by angle 5pi/6 about point Q. Point Z is the reflection of point J across line Y. Point M is the orthocenter of triangle ZJQ. Let H ... | 6.46 | MATH |
[
{
"content": "NB = 7. Let E be the reflection of point B across point N. Point R is obtained by rotating point N by angle pi/12 about point E. Let I be the rotation of point R by angle pi around point E. Let V be the midpoint of segment RN. Let U be the incenter of triangle NBI. Find the circumradius of triangl... | 65.14 | MATH |
[
{
"content": "JE = 3. Let F be the midpoint of segment EJ. Let V be the rotation of point J by angle pi/2 around point F. Let D be the line through point J perpendicular to segment EV. Point X is the midpoint of segment FE. Point Z is the reflection of point E across line D. Point G is the reflection of point X... | 2.25 | MATH |
[
{
"content": "LE = 3. Point Q is obtained by rotating point E by angle 3pi/4 about point L. Let U be the reflection of point Q across point E. Point J is the reflection of point U across segment LE. Let X be the midpoint of segment LE. What is the length of segment XJ? Express your answer as a decimal number ro... | 6.95 | MATH |
[
{
"content": "CO = 3. Point K is obtained by rotating point O by angle pi/6 about point C. Let L be the rotation of point C by angle pi/3 around point O. Point N is the midpoint of segment KO. Let H be the midpoint of segment OL. Point G is the reflection of point N across point C. Find the inradius of triangle... | 1.04 | MATH |
[
{
"content": "Let FX = 1. Let L be the rotation of point X by angle pi/2 around point F. Point P is obtained by rotating point F by angle 11pi/12 about point X. Circle G is the incircle of triangle PXL. Let C be the orthocenter of triangle PXL. Let V be the circumcenter of triangle PXL. Let W be the inversion o... | 0.25 | MATH |
[
{
"content": "CL = 10. Let H be the line through points L and C. Point M lies on line H at distance 4 from point L. Point B is obtained by rotating point L by angle pi/12 about point M. Point N is the reflection of point B across line H. Let Q be the reflection of point L across point B. Line R passes through p... | 4.15 | MATH |
[
{
"content": "GT = 4. J is constructed so that TJ = 5. Let U be the reflection of point J across point T. Let X be the midpoint of segment GU. Let O be the midpoint of segment JG. What is the distance between points O and X? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the ans... | 5.0 | MATH |
[
{
"content": "SL = 3. Point I is obtained by rotating point L by angle 3pi/4 about point S. Point V is the midpoint of segment LI. Let Q be the midpoint of segment VL. Let N be the line through points L and S. Point Z is the midpoint of segment QS. Point X is the orthocenter of triangle QZI. Point P is the refl... | 4.24 | MATH |
[
{
"content": "EK = 9. Point Y is obtained by rotating point K by angle pi/4 about point E. Point T is the midpoint of segment YK. Point B is the reflection of point K across point Y. Point N is the midpoint of segment BT. Point X is the reflection of point T across segment NE. Point U is the incenter of triangl... | 1.63 | MATH |
[
{
"content": "Let LV = 3. Point G is obtained by rotating point L by angle 5pi/6 about point V. Line E is the perpendicular bisector of segment GL. Line Y is the reflection of line E across point G. Line S is the reflection of line Y across line E. Let A be the midpoint of segment LV. Point M is the circumcente... | 333.06 | MATH |
[
{
"content": "RX = 9. Point W is obtained by rotating point R by angle 11pi/12 about point X. Point N is the midpoint of segment XR. Let Z be the midpoint of segment WR. Point H is obtained by rotating point W by angle 5pi/12 about point Z. Let Y be the reflection of point W across point R. Let B be the angle b... | 7.13 | MATH |
[
{
"content": "UF = 4. Point D is the midpoint of segment FU. Point T is obtained by rotating point U by angle 11pi/12 about point F. Let Q be the midpoint of segment FT. Point C is the reflection of point U across segment TD. Line J is the angle bisector of angle CQU. Point I is the reflection of point U across... | 0.0 | MATH |
[
{
"content": "Let LN = 7. Let B be the rotation of point L by angle 7pi/12 around point N. Point Q is the reflection of point N across segment BL. Point G is the reflection of point L across point B. Point S is the reflection of point Q across point B. What is the inradius of triangle GSN? Express your answer a... | 1.34 | MATH |
[
{
"content": "Let WL = 4. Let T be the reflection of point L across point W. Let R be the rotation of point W by angle 11pi/12 around point L. Point Z is the orthocenter of triangle TWR. Point F is the midpoint of segment RW. Point J is the orthocenter of triangle RLZ. Find the length of segment FJ. Express you... | 20.22 | MATH |
[
{
"content": "RS = 10. Let D be the midpoint of segment SR. Point Y is obtained by rotating point S by angle pi/12 about point R. Let Q be the line through points Y and D. Point E is the reflection of point S across line Q. Let T be the midpoint of segment YE. Find the length of segment TD. Express your answer ... | 5.0 | MATH |
[
{
"content": "Let KU = 3. Point H is the reflection of point U across point K. Let R be the line through points K and U. Let G be the rotation of point U by angle 2pi/3 around point H. Let F be the line through point G parallel to line R. Let V be the reflection of point G across point U. Let L be the rotation ... | 12.33 | MATH |
[
{
"content": "ZO = 7. Let B be the midpoint of segment ZO. Let V be the rotation of point B by angle pi/4 around point O. Let X be the midpoint of segment BZ. Let J be the midpoint of segment ZX. Line W passes through point V perpendicular to segment XZ. Point L is the reflection of point J across line W. Let T... | 1.68 | MATH |
[
{
"content": "SN = 8. Let X be the midpoint of segment NS. Let K be the rotation of point N by angle pi/12 around point X. Let H be the line through points K and S. Line T passes through point N parallel to line H. Point Q is the reflection of point N across point K. Point L is the reflection of point Q across ... | 1.6 | MATH |
[
{
"content": "OP = 5. Let Y be the line through points O and P. Let H be the perpendicular bisector of segment OP. Let J be the midpoint of segment PO. Point X is the reflection of point J across point P. Line D is the reflection of line H across point P. Line K passes through point O perpendicular to line Y. P... | 18.39 | MATH |
[
{
"content": "DT = 2. Let C be the rotation of point D by angle 3pi/4 around point T. Let Y be the circumcenter of triangle TCD. Point R is the incenter of triangle TCD. Let Z be the line through point Y perpendicular to segment TC. Point Q is the reflection of point T across line Z. What is the length of segme... | 0.44 | MATH |
[
{
"content": "Let EP = 6. Line V is the perpendicular bisector of segment PE. Point L lies on line V. Point F is obtained by rotating point E by angle 11pi/12 about point L. Let W be the midpoint of segment EP. Let G be the midpoint of segment FP. Let Z be the midpoint of segment PL. Find the measure of angle G... | 2.88 | MATH |
[
{
"content": "Let CN = 4. Let E be the rotation of point N by angle 5pi/12 around point C. Let L be the reflection of point C across point N. Point U is the midpoint of segment CE. Let F be the orthocenter of triangle LEN. Let K be the reflection of point N across point F. Point H is the circumcenter of triangl... | 7.39 | MATH |
[
{
"content": "Let SM = 4. Line X is the perpendicular bisector of segment MS. Point F is obtained by rotating point S by angle pi/4 about point M. Point R is the reflection of point F across line X. Let J be the angle bisector of angle FRM. Point C is the reflection of point R across point M. Point H is the ref... | 14.66 | MATH |
[
{
"content": "RL = 9. Line U is the perpendicular bisector of segment LR. Let E be the line through point L parallel to line U. Let C be the midpoint of segment RL. Point P is obtained by rotating point L by angle 3pi/4 about point R. Line K passes through point P parallel to segment LR. Point A is the reflecti... | 10.47 | MATH |
[
{
"content": "Let MG = 3. Let E be the rotation of point M by angle 5pi/6 around point G. Point V is the midpoint of segment EG. Let D be the incenter of triangle EGM. Let S be the centroid of triangle EGM. What is the measure of angle VDS, in radians? Express your answer as a decimal number rounded to 2 decima... | 0.09 | MATH |
[
{
"content": "SG = 12. Point L is obtained by rotating point S by angle pi/2 about point G. Point Z is obtained by rotating point S by angle pi/2 about point L. Point A is the circumcenter of triangle ZSL. Line R is the angle bisector of angle ZAG. Point U is the reflection of point S across line R. What is the... | 97.26 | MATH |
[
{
"content": "EJ = 6. Let C be the rotation of point J by angle 5pi/12 around point E. Point G is the reflection of point C across segment EJ. Point Y is the reflection of point J across point G. Point Z is the incenter of triangle EJC. Let H be the midpoint of segment JC. What is the measure of angle ZHY, in r... | 6.7 | MATH |
[
{
"content": "SB = 9. Let R be the rotation of point S by angle 7pi/12 around point B. Let Z be the reflection of point B across point R. Point D is the centroid of triangle BSR. Point M is the orthocenter of triangle BSR. Find the measure of angle ZDM, in radians. Express your answer as a decimal number rounde... | 53.4 | MATH |
[
{
"content": "SO = 10. Let T be the rotation of point O by angle 2pi/3 around point S. Let R be the reflection of point T across point O. Let U be the reflection of point S across point T. Let I be the reflection of point S across point O. What is the circumradius of triangle URI? Express your answer as a decim... | 43.59 | MATH |
[
{
"content": "JG = 2. Let I be the rotation of point G by angle 7pi/12 around point J. Point N is the midpoint of segment GI. Point R is the centroid of triangle GIJ. Point Y is the reflection of point R across segment GI. Point B is the reflection of point N across segment JG. What is the distance between poin... | 2.27 | MATH |
[
{
"content": "Let XG = 6. Point B is obtained by rotating point X by angle pi about point G. Let Z be the rotation of point B by angle 7pi/12 around point G. Let U be the midpoint of segment ZG. Point V is on segment UX. Let W be the midpoint of segment UB. What is the measure of angle VWG, in radians? Express ... | 4.35 | MATH |
[
{
"content": "VD = 11. Point U is obtained by rotating point V by angle 3pi/4 about point D. Line H is the angle bisector of angle VUD. Let R be the midpoint of segment VD. Point A is the reflection of point R across segment DU. Point P is the reflection of point V across line H. Find the distance between point... | 6.68 | MATH |
[
{
"content": "NO = 1. Point Y is obtained by rotating point O by angle pi/12 about point N. Let R be the midpoint of segment ON. Point E is the reflection of point R across point N. Let K be the orthocenter of triangle YRE. Find the distance between points K and Y. Express your answer as a decimal number rounde... | 2.9 | MATH |
[
{
"content": "VU = 8. Let J be the rotation of point V by angle pi/4 around point U. Let B be the midpoint of segment VU. Point T is the orthocenter of triangle BVJ. Let K be the midpoint of segment VJ. Find the measure of angle UTK, in radians. Express your answer as a decimal number rounded to 2 decimal place... | 5.66 | MATH |
[
{
"content": "HQ = 6. Let Y be the midpoint of segment QH. Point A is the reflection of point Y across point H. Point B is obtained by rotating point A by angle 3pi/4 about point Y. Let K be the midpoint of segment BH. Let R be the line through point K perpendicular to segment AB. Point V is the reflection of p... | 4.2 | MATH |
[
{
"content": "Let RY = 8. Let H be the vector from point R to point Y. Point O is obtained by rotating point Y by angle 3pi/4 about point R. Let L be point O translated by vector H. Point K is the midpoint of segment RY. Let D be the reflection of point K across point Y. Point M is the reflection of point K acr... | 3.31 | MATH |
[
{
"content": "Let BN = 12. Let G be the rotation of point B by angle 2pi/3 around point N. Point W is the reflection of point B across point N. Let I be the midpoint of segment NW. Line V is the perpendicular bisector of segment NG. Let K be the midpoint of segment IW. Point L is the reflection of point K acros... | 6.25 | MATH |
[
{
"content": "Let RP = 9. Let S be the rotation of point P by angle 11pi/12 around point R. Let N be the perpendicular bisector of segment SP. Point O is the reflection of point S across point R. Line I is the perpendicular bisector of segment SR. Let T be the reflection of line I across line N. Point Z is the ... | 9.16 | MATH |
[
{
"content": "Let TL = 12. Point P is obtained by rotating point T by angle pi/4 about point L. Point M is the orthocenter of triangle TPL. Circle V is the incircle of triangle TPL. Point Y is the reflection of point M across segment PL. Let K be the inversion of point Y in circle V. Find the length of segment ... | 4.67 | MATH |
[
{
"content": "Let OH = 2. Let U be the rotation of point H by angle pi/6 around point O. Point V is obtained by rotating point H by angle 2pi/3 about point U. Point T is the midpoint of segment OV. Let K be the line through point U perpendicular to segment HO. Point R is the reflection of point V across line K.... | 1.83 | MATH |
[
{
"content": "DL = 10. Point B is the midpoint of segment LD. Let M be the perpendicular bisector of segment DL. Point R is on line M with |RD| = 4. Line X passes through point R perpendicular to segment DR. Point S is the midpoint of segment DR. Point C is the reflection of point B across line X. Find the leng... | 6.5 | MATH |
[
{
"content": "EV = 2. Point G is the reflection of point E across point V. Let P be the reflection of point E across point G. Point Y is obtained by rotating point G by angle 7pi/12 about point V. Point Q is obtained by rotating point P by angle 5pi/12 about point Y. Point J is the midpoint of segment YE. Let W... | 19.95 | MATH |
[
{
"content": "TA = 12. Point S is obtained by rotating point T by angle 5pi/12 about point A. Let X be the reflection of point T across point A. Point U is the midpoint of segment AS. Point I is the midpoint of segment UX. What is the measure of angle STI, in radians? Express your answer as a decimal number rou... | 86.93 | MATH |
[
{
"content": "OF = 5. Point Z is obtained by rotating point O by angle 2pi/3 about point F. Point Y is the incenter of triangle OZF. Let I be the centroid of triangle OZF. Let S be the incircle of triangle OZF. Circle B is the reflection of circle S across point I. Let D be the inversion of point I in circle B.... | 1.86 | MATH |
[
{
"content": "UB = 3. Let E be the rotation of point B by angle 5pi/12 around point U. Let Z be the vector from point B to point U. Let H be point U translated by vector Z. Point O is the midpoint of segment EH. Point P is the reflection of point U across point H. Let Q be the midpoint of segment PE. Find the c... | 6.48 | MATH |
[
{
"content": "NW = 8. Point Y is obtained by rotating point W by angle 3pi/4 about point N. Line P passes through point N perpendicular to segment NY. Let Q be the reflection of point Y across point N. Let X be the reflection of point Q across point W. Point D is the reflection of point X across line P. Point M... | 9.76 | MATH |
[
{
"content": "Let IS = 11. Let Z be the rotation of point S by angle 3pi/4 around point I. Point F is obtained by rotating point Z by angle 2pi/3 about point S. Let T be the incenter of triangle ZFI. Point L is the reflection of point S across point I. Let A be the circumcenter of triangle ZFI. Find the measure... | 18.57 | MATH |
[
{
"content": "ZC = 8. Let U be the reflection of point Z across point C. Point K is obtained by rotating point U by angle 11pi/12 about point Z. Point H is the reflection of point K across segment ZU. Let F be the centroid of triangle ZUK. Point X is the reflection of point Z across point H. Find the distance b... | 32.56 | MATH |
[
{
"content": "Let CJ = 8. Line P is the perpendicular bisector of segment JC. Let H be the rotation of point C by angle 11pi/12 around point J. Point M is the reflection of point H across line P. Let X be the centroid of triangle CMH. Point E is the reflection of point X across line P. Let L be the midpoint of ... | 2.55 | MATH |
[
{
"content": "QJ = 2. Let W be the rotation of point J by angle pi/4 around point Q. Let U be the rotation of point W by angle 2pi/3 around point Q. Let C be the rotation of point Q by angle 11pi/12 around point U. Point I is the midpoint of segment CU. Line A is the perpendicular bisector of segment CI. Let H ... | 0.47 | MATH |
[
{
"content": "Let UJ = 4. Point P is the reflection of point U across point J. Let F be the rotation of point J by angle pi/3 around point U. Point E is the midpoint of segment JF. Let I be the midpoint of segment EP. Point Y is the circumcenter of triangle EUF. Point H is the midpoint of segment UY. Find the m... | 2.02 | MATH |
[
{
"content": "LZ = 12. Let B be the midpoint of segment ZL. Let E be the rotation of point L by angle 7pi/12 around point Z. Point P is the reflection of point E across point Z. Let I be the midpoint of segment PZ. Let F be the orthocenter of triangle PIB. Find the distance between points F and L. Express your ... | 19.67 | MATH |
[
{
"content": "Let VD = 5. Let K be the rotation of point V by angle pi/4 around point D. Let G be the rotation of point K by angle 2pi/3 around point V. Line W is the perpendicular bisector of segment DV. Let X be the reflection of line W through point D. Point P is the reflection of point V across point K. Poi... | 1.09 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.