messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let BR = 4. Line M is the perpendicular bisector of segment BR. Point O is on line M with |OB| = 5. Line N passes through point R parallel to line M. Let S be the perpendicular bisector of segment OB. Let E be the reflection of line S across line N. Let A be the reflection of point O across point ... | 2.57 | MATH |
[
{
"content": "FJ = 7. Let I be the rotation of point F by angle 5pi/12 around point J. Line U passes through points I and F. Point W is obtained by rotating point I by angle pi/4 about point F. Let X be the line through point W perpendicular to line U. Point Y is the midpoint of segment FW. Point Z is the refle... | 3.99 | MATH |
[
{
"content": "CA = 8. Let G be the rotation of point A by angle pi/3 around point C. Point E is the midpoint of segment CA. Point H is the reflection of point E across point C. Let M be the reflection of point C across point H. Let I be the midpoint of segment GE. Find the measure of angle MHI, in radians. Expr... | 6.93 | MATH |
[
{
"content": "SN = 2. Let L be the rotation of point S by angle 2pi/3 around point N. Let D be the reflection of point N across point L. Let X be the rotation of point N by angle 5pi/12 around point L. Let A be the midpoint of segment LX. Line T is the angle bisector of angle XSN. Point E is the reflection of p... | 11.59 | MATH |
[
{
"content": "Let ZD = 3. Let U be the midpoint of segment ZD. Let W be the rotation of point U by angle 11pi/12 around point D. Let I be the rotation of point Z by angle 5pi/12 around point W. Point F is the reflection of point Z across point D. Point Y is the midpoint of segment DF. Point K is the midpoint of... | 3.59 | MATH |
[
{
"content": "SP = 2. Let A be the rotation of point P by angle 3pi/4 around point S. Let E be the midpoint of segment PS. Let B be the incircle of triangle PAS. Let V be the inversion of point E in circle B. Let F be the midpoint of segment AE. What is the measure of angle FVP, in radians? Express your answer ... | 0.26 | MATH |
[
{
"content": "AB = 4. Point F is the midpoint of segment BA. Point L is obtained by rotating point A by angle 3pi/4 about point F. Point V is obtained by rotating point L by angle pi/6 about point A. Point J is obtained by rotating point B by angle 11pi/12 about point A. Let Y be the angle bisector of angle BVJ... | 1.01 | MATH |
[
{
"content": "Let BE = 11. Point Y is the midpoint of segment EB. Let G be the rotation of point E by angle 11pi/12 around point B. Point W is the reflection of point B across point G. Let I be the angle bisector of angle BWE. Point D is the reflection of point E across line I. Point A is the reflection of poin... | 20.56 | MATH |
[
{
"content": "Let JF = 3. Let V be the rotation of point J by angle pi/3 around point F. Let P be the midpoint of segment JF. Point Q is the reflection of point V across point J. Point Y is the incenter of triangle VPJ. What is the circumradius of triangle YQF? Express your answer as a decimal number rounded to... | 2.82 | MATH |
[
{
"content": "Let FJ = 8. Let N be the rotation of point J by angle 5pi/6 around point F. Let S be the centroid of triangle NFJ. Let R be the rotation of point N by angle pi/12 around point F. Let W be the orthocenter of triangle NFJ. Let A be the midpoint of segment RF. Point O is obtained by rotating point W ... | 80.45 | MATH |
[
{
"content": "YQ = 6. Let X be the reflection of point Q across point Y. Let H be the rotation of point X by angle 11pi/12 around point Q. Point Z is obtained by rotating point H by angle 5pi/6 about point X. Let F be the midpoint of segment XH. Point N is the circumcenter of triangle HZF. Point R is the reflec... | 10.1 | MATH |
[
{
"content": "Let MN = 10. Let G be the rotation of point N by angle 5pi/12 around point M. Point C is the circumcenter of triangle NMG. Let J be the circumcircle of triangle NMG. Let V be the reflection of point C across point G. Let U be the inversion of point V in circle J. Find the length of segment UC. Exp... | 3.55 | MATH |
[
{
"content": "Let QV = 4. Let C be the rotation of point V by angle 11pi/12 around point Q. Point B is obtained by rotating point C by angle pi/6 about point Q. Let Z be the reflection of point Q across point V. Let U be the midpoint of segment BV. Point M is the midpoint of segment BC. Point W is the reflectio... | 0.26 | MATH |
[
{
"content": "Let KJ = 5. Let P be the midpoint of segment JK. Let W be the rotation of point K by angle 11pi/12 around point P. Let L be the reflection of point P across point K. Let N be the reflection of point W across point K. Point U is the midpoint of segment PW. Let Z be the reflection of point U across ... | 11.15 | MATH |
[
{
"content": "GQ = 3. Point F is obtained by rotating point G by angle 3pi/4 about point Q. Let P be the reflection of point Q across point G. Point H is the reflection of point G across point Q. Line Y is the perpendicular bisector of segment QF. Point M is obtained by rotating point F by angle 2pi/3 about poi... | 6.66 | MATH |
[
{
"content": "MX = 3. Point H is the midpoint of segment XM. Let W be the rotation of point M by angle 5pi/12 around point H. Let A be the rotation of point X by angle pi/3 around point M. Point I is the reflection of point H across segment WA. Point O is the midpoint of segment MW. Let V be the incenter of tri... | 0.34 | MATH |
[
{
"content": "Let OZ = 11. Let D be the rotation of point Z by angle 2pi/3 around point O. Let U be the midpoint of segment ZO. Point V is the reflection of point O across segment UD. Point W is the reflection of point Z across segment UD. Find the circumradius of triangle VWO. Express your answer as a decimal ... | 5.5 | MATH |
[
{
"content": "AK = 2. Point N is obtained by rotating point A by angle 7pi/12 about point K. Point E is the reflection of point A across point N. Point Q is the midpoint of segment EN. Let O be the midpoint of segment QN. Point W is the incenter of triangle ENK. Find the distance between points O and W. Express... | 0.77 | MATH |
[
{
"content": "OV = 4. Let B be the line through points O and V. Line R passes through point V perpendicular to line B. Point X is the reflection of point O across line R. Let C be the reflection of point O across point X. Point L lies on line R at distance 8 from point V. Point Q is the reflection of point L ac... | 31.03 | MATH |
[
{
"content": "FW = 12. Let P be the rotation of point F by angle pi/6 around point W. Let I be the angle bisector of angle PFW. Point J is the reflection of point W across line I. Let Q be the midpoint of segment WJ. What is the distance between points J and Q? Express your answer as a decimal number rounded to... | 7.31 | MATH |
[
{
"content": "Let JW = 9. Point I is obtained by rotating point J by angle pi/3 about point W. Point Y is the reflection of point I across point J. Let T be the incenter of triangle WIY. Point H is the centroid of triangle WIY. What is the length of segment HT? Express your answer as a decimal number rounded to... | 1.92 | MATH |
[
{
"content": "PJ = 8. V is constructed so that JV = 8. Point Q is the midpoint of segment PJ. Let B be the midpoint of segment VP. Point Y is the centroid of triangle VPQ. What is the length of segment YB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format... | 1.33 | MATH |
[
{
"content": "Let GJ = 1. Point F is obtained by rotating point J by angle pi/6 about point G. Point M is the circumcenter of triangle GJF. Let P be the line through point M parallel to segment JF. Point R is the reflection of point J across line P. What is the length of segment MR? Express your answer as a dec... | 0.41 | MATH |
[
{
"content": "Let GW = 4. Let S be the rotation of point W by angle pi/2 around point G. Let R be the perpendicular bisector of segment WG. Circle C is the incircle of triangle WGS. Let N be the reflection of circle C across line R. Point J is the midpoint of segment SW. Let O be the inversion of point W in cir... | 2.0 | MATH |
[
{
"content": "WN = 8. Point C is obtained by rotating point N by angle pi/3 about point W. Point B is the reflection of point C across point N. Point X is obtained by rotating point N by angle 5pi/6 about point C. Point H is the reflection of point W across point N. Let Q be the reflection of point H across poi... | 259.14 | MATH |
[
{
"content": "Let IF = 9. Let T be the midpoint of segment IF. Point X is obtained by rotating point I by angle pi/6 about point F. Point H is the reflection of point F across point X. Line L is the angle bisector of angle FHT. Point O is the midpoint of segment TF. Point R is the reflection of point O across l... | 8.03 | MATH |
[
{
"content": "Let RM = 12. Let N be the rotation of point R by angle 7pi/12 around point M. Point J is the midpoint of segment RM. Let K be the circumcenter of triangle MNJ. Let S be the reflection of point R across point K. Point F is the reflection of point N across point S. Find the distance between points F... | 29.29 | MATH |
[
{
"content": "Let EA = 11. Let O be the rotation of point E by angle 7pi/12 around point A. Let R be the rotation of point E by angle 5pi/6 around point A. Point W is the incenter of triangle ARO. Point N is the reflection of point W across segment AR. Point C is the reflection of point W across point N. Let D ... | 8.54 | MATH |
[
{
"content": "Let OH = 3. Let R be the rotation of point O by angle pi/2 around point H. Let W be the reflection of point R across point O. Point C is the reflection of point R across point W. Point T is the reflection of point R across segment HO. Point D is the reflection of point W across segment HO. Find th... | 54.0 | MATH |
[
{
"content": "Let UK = 6. Let D be the midpoint of segment UK. Let V be the rotation of point K by angle pi/6 around point D. Point X is the midpoint of segment VU. Let G be the line through points U and K. Point R is the reflection of point X across line G. Find the inradius of triangle DXR. Express your answe... | 0.1 | MATH |
[
{
"content": "JB = 1. Let L be the rotation of point J by angle 3pi/4 around point B. Point T is the midpoint of segment LB. Let C be the circumcircle of triangle BJL. Let F be the circumcenter of triangle BJL. Let H be the inversion of point F in circle C. What is the length of segment HT? Express your answer ... | 0.69 | MATH |
[
{
"content": "WY = 1. Let V be the reflection of point W across point Y. Let X be the angle bisector of angle VYW. Line S is the perpendicular bisector of segment YW. Point L is obtained by rotating point Y by angle pi/4 about point W. Point F is the reflection of point L across point W. Point Q is obtained by ... | 0.38 | MATH |
[
{
"content": "Let BN = 1. Let L be the rotation of point B by angle 11pi/12 around point N. Point I is obtained by rotating point N by angle pi/2 about point B. Let J be the reflection of point B across point I. Let Q be the midpoint of segment LN. Point E is the reflection of point Q across segment JB. Let U b... | 1.72 | MATH |
[
{
"content": "Let LN = 6. Point D is obtained by rotating point L by angle pi/2 about point N. Let A be the midpoint of segment LD. Line Q passes through point L perpendicular to segment ND. Circle S is the circumcircle of triangle DAN. Point M is the reflection of point D across line Q. Point W is the circumce... | 3.6 | MATH |
[
{
"content": "Let LC = 2. Let Q be the line through points L and C. Point A is the reflection of point L across point C. Line D is the perpendicular bisector of segment AC. Point R is on line D with |RC| = 9. Point T is the reflection of point R across line Q. Point F is the reflection of point A across point T... | 1.39 | MATH |
[
{
"content": "Let VR = 8. Point Q is obtained by rotating point V by angle 3pi/4 about point R. Let K be the midpoint of segment RQ. Let W be the orthocenter of triangle KVQ. Let P be the reflection of point R across point V. Find the distance between points P and W. Express your answer as a decimal number roun... | 35.09 | MATH |
[
{
"content": "HZ = 2. Point I is obtained by rotating point H by angle pi/3 about point Z. Point P is the reflection of point I across point H. Line E is the perpendicular bisector of segment IP. Let J be the midpoint of segment PZ. Point W is the reflection of point Z across line E. Find the circumradius of tr... | 1.0 | MATH |
[
{
"content": "Let ZY = 6. Point A is obtained by rotating point Y by angle 3pi/4 about point Z. Line E is the perpendicular bisector of segment AZ. Point S is the reflection of point Z across point A. Point W is the reflection of point S across line E. Point N is the midpoint of segment WY. Let L be the reflect... | 6.36 | MATH |
[
{
"content": "Let BN = 3. Point J is the reflection of point B across point N. Point A is obtained by rotating point B by angle pi/6 about point N. Let M be the reflection of point N across point B. Let U be the orthocenter of triangle AMJ. Point P is the midpoint of segment AM. Find the measure of angle NUP, i... | 26.32 | MATH |
[
{
"content": "PG = 4. Let K be the rotation of point G by angle pi/4 around point P. Point F is obtained by rotating point P by angle pi/12 about point K. Let C be the orthocenter of triangle GFP. Point M is the incenter of triangle GFP. Point Q is the reflection of point M across segment FK. What is the length... | 3.74 | MATH |
[
{
"content": "Let HL = 4. Point R is obtained by rotating point H by angle 2pi/3 about point L. Point D is the reflection of point R across point L. Point K is the circumcenter of triangle LHR. Let S be the midpoint of segment KD. What is the distance between points S and K? Express your answer as a decimal num... | 2.4 | MATH |
[
{
"content": "Let UK = 2. Let H be the rotation of point U by angle 5pi/6 around point K. Let P be the midpoint of segment KH. Let C be the circumcircle of triangle UHK. Let N be the reflection of circle C through point P. Let Z be the inversion of point P in circle N. Let R be the incenter of triangle UHK. Fin... | 0.93 | MATH |
[
{
"content": "Let CA = 8. Line M is the perpendicular bisector of segment CA. Line W is the reflection of line M across point A. Point U lies on line M at distance 5 from point A. Point G is the reflection of point A across line W. Point T is the midpoint of segment AU. Let V be the orthocenter of triangle UAG.... | 7.71 | MATH |
[
{
"content": "Let KD = 4. Let C be the rotation of point K by angle pi around point D. Line G is the angle bisector of angle CKD. Let A be the rotation of point C by angle pi/3 around point K. Let M be the rotation of point K by angle pi/2 around point C. Let F be the midpoint of segment MK. Point R is the midp... | 41.37 | MATH |
[
{
"content": "UT = 7. Point E is the midpoint of segment TU. Let J be the rotation of point T by angle pi/4 around point E. Point R is obtained by rotating point J by angle pi about point U. Let V be the rotation of point J by angle pi/2 around point U. Point P is obtained by rotating point R by angle 3pi/4 abo... | 20.39 | MATH |
[
{
"content": "Let NY = 10. Line T is the perpendicular bisector of segment NY. Point U lies on line T at distance 1 from point Y. Let L be the midpoint of segment NU. Line D passes through point N parallel to line T. Let E be the incenter of triangle YNU. Point R is the circumcenter of triangle YNU. Point X is ... | 0.63 | MATH |
[
{
"content": "Let WC = 3. Let E be the midpoint of segment WC. Let D be the rotation of point W by angle pi/6 around point C. Point H is the reflection of point D across point W. Point A is the midpoint of segment DE. Let T be the incenter of triangle CHA. Find the distance between points H and T. Express your ... | 2.18 | MATH |
[
{
"content": "EI = 10. Point F is obtained by rotating point I by angle pi/2 about point E. Point T is the midpoint of segment FE. Point R is the incenter of triangle TFI. Let K be the orthocenter of triangle TFI. What is the distance between points K and R? Express your answer as a decimal number rounded to 2 ... | 8.97 | MATH |
[
{
"content": "Let BH = 4. Line O is the perpendicular bisector of segment HB. Point C is on line O with |CB| = 8. Point F is the reflection of point H across point B. Point Y is the reflection of point F across line O. Point D is the centroid of triangle HCF. What is the length of segment DY? Express your answe... | 7.8 | MATH |
[
{
"content": "CB = 11. Point H is the midpoint of segment CB. Point Y is the reflection of point B across point C. Let S be the rotation of point B by angle 3pi/4 around point Y. Line Q passes through point B perpendicular to segment SH. Line U passes through point C parallel to line Q. Point G is the intersect... | 2.4 | MATH |
[
{
"content": "Let MH = 8. Let B be the rotation of point H by angle pi/4 around point M. Line V passes through points B and H. Point G is obtained by rotating point B by angle 5pi/6 about point H. Point I is the reflection of point M across line V. Line K passes through point M parallel to line V. Point P is th... | 60.99 | MATH |
[
{
"content": "RI = 7. Point V is obtained by rotating point I by angle pi/4 about point R. Point W is the reflection of point V across point R. Let A be the perpendicular bisector of segment RV. Point O is the reflection of point W across line A. Let J be the circumcenter of triangle WVI. Let X be the angle bis... | 18.67 | MATH |
[
{
"content": "NI = 9. Let P be the reflection of point I across point N. Let O be the reflection of point P across point I. Let M be the midpoint of segment NO. Let B be the rotation of point M by angle 11pi/12 around point O. Line C passes through points B and O. Point H is the reflection of point N across lin... | 12.22 | MATH |
[
{
"content": "Let RL = 7. Let U be the rotation of point R by angle pi/6 around point L. Let W be the rotation of point R by angle pi/2 around point U. Point P is the incenter of triangle WLU. Point H is the midpoint of segment PW. What is the circumradius of triangle HRW? Express your answer as a decimal numbe... | 3.05 | MATH |
[
{
"content": "XN = 7. Let K be the rotation of point X by angle pi/3 around point N. Let J be the rotation of point X by angle pi/2 around point K. Point S is the reflection of point K across point J. Let Q be the reflection of point N across point J. Point M is the reflection of point N across point S. Find th... | 38.43 | MATH |
[
{
"content": "Let SX = 10. Point D is the midpoint of segment SX. Let W be the perpendicular bisector of segment XD. Let I be the line through point X parallel to line W. Let T be the midpoint of segment DS. Point Y is the reflection of point S across line I. Point B is obtained by rotating point X by angle 5pi... | 0.21 | MATH |
[
{
"content": "ID = 1. Let S be the rotation of point I by angle 5pi/12 around point D. Let B be the circumcenter of triangle SDI. Point O is the reflection of point B across segment SD. Point R is the reflection of point B across segment IS. Find the measure of angle ROI, in radians. Express your answer as a de... | 0.35 | MATH |
[
{
"content": "RH = 3. Point K is obtained by rotating point R by angle 5pi/6 about point H. Let Y be the reflection of point K across point R. Let Q be the midpoint of segment RK. Let S be the midpoint of segment QY. Find the distance between points Q and S. Express your answer as a decimal number rounded to 2 ... | 4.35 | MATH |
[
{
"content": "EC = 11. Let N be the perpendicular bisector of segment EC. Let D be the reflection of point C across point E. Point B is on line N with |BC| = 12. Point I is the reflection of point D across line N. Point S is the reflection of point B across segment DC. Point U is the reflection of point I acros... | 4.03 | MATH |
[
{
"content": "Let QF = 5. Point U is obtained by rotating point F by angle 7pi/12 about point Q. Let Y be the centroid of triangle UFQ. Line X passes through point F parallel to segment QU. Let A be the midpoint of segment QU. Line I passes through point Y parallel to line X. Point S is the intersection of line... | 1.31 | MATH |
[
{
"content": "QH = 2. Point S is the reflection of point H across point Q. Let R be the rotation of point H by angle 5pi/12 around point S. Let W be the rotation of point S by angle 2pi/3 around point H. Let G be the midpoint of segment SR. Let M be the angle bisector of angle GWQ. Point K is the reflection of ... | 2.71 | MATH |
[
{
"content": "LX = 3. Line N passes through points L and X. Point U is obtained by rotating point L by angle 3pi/4 about point X. Let G be the midpoint of segment XU. Point J is the reflection of point G across line N. Let R be the midpoint of segment JL. Point D is the orthocenter of triangle XJR. Point Q is t... | 0.48 | MATH |
[
{
"content": "Let MA = 12. Point Z is the midpoint of segment MA. Let K be the rotation of point A by angle 11pi/12 around point Z. Point S is the incenter of triangle MKZ. Point X is the midpoint of segment ZS. Point Y is the centroid of triangle MKZ. What is the distance between points Y and X? Express your a... | 1.33 | MATH |
[
{
"content": "Let HD = 11. Point F is obtained by rotating point H by angle pi/2 about point D. Line Z is the perpendicular bisector of segment FH. Point T is the circumcenter of triangle DFH. Let N be the reflection of point F across point T. Point K is the reflection of point N across line Z. Let U be the inc... | 9.24 | MATH |
[
{
"content": "FT = 4. Point E is the reflection of point F across point T. Point G is obtained by rotating point E by angle pi/2 about point F. Let C be the rotation of point G by angle 3pi/4 around point F. Point I is the reflection of point C across point F. Point N is the reflection of point I across point E... | 1.9 | MATH |
[
{
"content": "RJ = 3. Point M is obtained by rotating point J by angle pi/12 about point R. Let N be the rotation of point M by angle 2pi/3 around point R. Let T be the midpoint of segment JR. Point Q is the reflection of point N across point T. Find the inradius of triangle JNQ. Express your answer as a decima... | 0.38 | MATH |
[
{
"content": "RW = 10. Point M is obtained by rotating point W by angle pi/4 about point R. Point G is the midpoint of segment WM. Let K be the reflection of point G across point R. Let B be the incircle of triangle WKM. Point U is the inversion of point M with respect to circle B. Let L be the line through poi... | 14.18 | MATH |
[
{
"content": "TH = 10. Point B is obtained by rotating point T by angle 3pi/4 about point H. Let Z be the perpendicular bisector of segment TB. Point O is obtained by rotating point T by angle pi about point B. Circle V is the circumcircle of triangle OHB. Let K be the reflection of circle V across line Z. Poin... | 15.03 | MATH |
[
{
"content": "Let R be the midpoint of segment Z92L. Point B is the orthocenter of triangle L. Let F be the midpoint of segment UR. Let Z be the reflection of point L across point F. Point G is the midpoint of segment BF. What is the length of segment ZG? Express your answer as a decimal number rounded to 2 dec... | 0.89 | MATH |
[
{
"content": "YH = 11. Point D is the reflection of point Y across point H. Point K is obtained by rotating point H by angle pi/2 about point D. Line V passes through points D and H. Let N be the line through points K and H. Line B is the reflection of line N across line V. Point X is the midpoint of segment DH... | 60.5 | MATH |
[
{
"content": "Let VK = 8. Let F be the rotation of point K by angle 5pi/6 around point V. Let Q be the midpoint of segment FK. Point N is the midpoint of segment QK. Let J be the midpoint of segment NK. Point O is the centroid of triangle QVN. Find the distance between points J and O. Express your answer as a d... | 4.56 | MATH |
[
{
"content": "HC = 12. Point N is obtained by rotating point C by angle 3pi/4 about point H. Point M is the midpoint of segment CN. Point B is the incenter of triangle NHC. Let T be the midpoint of segment BM. Point P lies on segment NH. What is the measure of angle PHT, in radians? Express your answer as a dec... | 1.18 | MATH |
[
{
"content": "Let UK = 3. Let V be the rotation of point K by angle pi/3 around point U. Point G is the midpoint of segment UK. Point B is the reflection of point G across segment VK. Find the inradius of triangle KGB. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in... | 0.35 | MATH |
[
{
"content": "GP = 6. Point D is obtained by rotating point G by angle 11pi/12 about point P. Let A be the midpoint of segment DP. Let N be the reflection of point G across point P. Let T be the midpoint of segment NA. Point V is the midpoint of segment PA. What is the measure of angle VGT, in radians? Express ... | 0.58 | MATH |
[
{
"content": "Let UL = 10. Let B be the reflection of point U across point L. Let N be the rotation of point B by angle 5pi/6 around point U. Line O passes through points U and N. Let UT = 4. Point S is the reflection of point B across line O. Let E be the perpendicular bisector of segment BL. Point F is the re... | 17.32 | MATH |
[
{
"content": "TK = 2. Point N is the midpoint of segment KT. Let P be the rotation of point K by angle 2pi/3 around point N. Point Z is the midpoint of segment PN. Point O is the reflection of point N across segment PT. Point D is the circumcenter of triangle ZPT. Find the measure of angle DPO, in radians. Expr... | 0.22 | MATH |
[
{
"content": "JP = 5. Point N is the reflection of point P across point J. Let U be the rotation of point P by angle pi/6 around point J. Line D is the angle bisector of angle UPJ. Line O is the angle bisector of angle UJP. Let A be the midpoint of segment JN. Let Y be the midpoint of segment JU. Line W passes ... | 9.16 | MATH |
[
{
"content": "Let UL = 9. Point M is the midpoint of segment UL. Let E be the angle bisector of angle UML. Point H is obtained by rotating point L by angle pi/12 about point U. Point P is obtained by rotating point M by angle 3pi/4 about point H. Line I passes through point L parallel to line E. Point G is the ... | 1.14 | MATH |
[
{
"content": "Let DL = 3. Let K be the rotation of point L by angle pi/4 around point D. Point P is the midpoint of segment LK. Let B be the reflection of point P across point K. Let A be the circumcenter of triangle DKL. Let I be the midpoint of segment BA. Find the distance between points D and I. Express you... | 2.58 | MATH |
[
{
"content": "TX = 3. Line N passes through points X and T. Point C is obtained by rotating point T by angle 5pi/12 about point X. Let G be the reflection of point X across point C. Let Y be the line through point C perpendicular to line N. Point O is on line Y. Let V be the midpoint of segment TG. Point W is t... | 0.73 | MATH |
[
{
"content": "MI = 2. Let J be the rotation of point I by angle pi/6 around point M. Point X is obtained by rotating point I by angle pi/12 about point M. Point B is the midpoint of segment MJ. Point E is the reflection of point X across segment IM. Point A is the reflection of point B across segment IM. Point ... | 0.26 | MATH |
[
{
"content": "Let JP = 6. Let D be the rotation of point P by angle pi/4 around point J. M is placed 1 units away from D. Let C be the rotation of point M by angle pi/6 around point P. Point S is the reflection of point C across segment PM. Point U is the reflection of point P across point S. Point R is the mid... | 2.09 | MATH |
[
{
"content": "Let UZ = 1. Let E be the reflection of point Z across point U. Let K be the rotation of point Z by angle pi/2 around point E. Point R is the circumcenter of triangle EKU. Point L is the orthocenter of triangle KRZ. Point X is the centroid of triangle KRZ. What is the measure of angle KXL, in radia... | 1.7 | MATH |
[
{
"content": "RO = 11. Let C be the line through points R and O. Point Y is obtained by rotating point O by angle 7pi/12 about point R. Let U be the perpendicular bisector of segment YR. Point L is the reflection of point Y across line C. Let I be the rotation of point Y by angle pi around point R. Let G be the... | 0.26 | MATH |
[
{
"content": "LK = 8. Point V is the reflection of point L across point K. Point D is obtained by rotating point K by angle pi/12 about point V. Point O is the midpoint of segment KD. Let M be the line through point O parallel to segment LK. Point Z is the reflection of point L across line M. Find the circumrad... | 1859.51 | MATH |
[
{
"content": "SB = 9. Let W be the rotation of point S by angle 7pi/12 around point B. Let C be the rotation of point W by angle pi/6 around point B. Point K is the midpoint of segment WS. Line N is the perpendicular bisector of segment KC. Point D is the reflection of point W across line N. Line I is the angle... | 35.67 | MATH |
[
{
"content": "Let LT = 1. Let R be the vector from point L to point T. Point E is obtained by rotating point T by angle 5pi/12 about point L. Point K is the translation of point T by vector R. Line F is the perpendicular bisector of segment LK. Let C be the midpoint of segment LE. Let O be the midpoint of segme... | 0.11 | MATH |
[
{
"content": "Let LG = 3. Point P is the reflection of point G across point L. Point J is obtained by rotating point P by angle 5pi/12 about point G. Point V is obtained by rotating point J by angle pi/6 about point P. Let Y be the perpendicular bisector of segment PV. Point O is the orthocenter of triangle PVG... | 4.26 | MATH |
[
{
"content": "ZU = 9. Let H be the reflection of point Z across point U. Point M is obtained by rotating point H by angle pi/4 about point Z. Point V is the centroid of triangle HMZ. Point Q is the midpoint of segment ZM. Point S is the midpoint of segment UV. Point Y is the reflection of point S across segment... | 5.35 | MATH |
[
{
"content": "ZG = 11. Point Q is the reflection of point Z across point G. Point J is obtained by rotating point G by angle 7pi/12 about point Z. Let F be the rotation of point Q by angle 11pi/12 around point G. Point X is the orthocenter of triangle FJG. Point W is the incenter of triangle FJG. Point D is the... | 0.38 | MATH |
[
{
"content": "Let HP = 12. Let I be the rotation of point H by angle pi/12 around point P. Point C is the midpoint of segment IP. Let Z be the midpoint of segment IC. Point T is the circumcenter of triangle ICH. What is the measure of angle TCZ, in radians? Express your answer as a decimal number rounded to 2 d... | 0.26 | MATH |
[
{
"content": "Let HS = 9. Line Z passes through points H and S. Point J is obtained by rotating point S by angle 11pi/12 about point H. Point G is the reflection of point J across point S. Point Y is the incenter of triangle GHJ. Let I be the reflection of line Z through point Y. Point C is the reflection of po... | 35.46 | MATH |
[
{
"content": "Let WO = 3. Point L is obtained by rotating point W by angle 11pi/12 about point O. Point S is the midpoint of segment OW. Let B be the incenter of triangle LOW. Point X is the reflection of point B across segment WL. Point U is the midpoint of segment SX. What is the length of segment XU? Express... | 0.77 | MATH |
[
{
"content": "Let BC = 9. Let L be the rotation of point C by angle 5pi/6 around point B. Let Q be the midpoint of segment CL. Let S be the midpoint of segment QL. Point Z is the reflection of point Q across segment BL. Find the measure of angle SBZ, in radians. Express your answer as a decimal number rounded t... | 5.74 | MATH |
[
{
"content": "UZ = 2. Let I be the reflection of point Z across point U. Let J be the vector from point Z to point I. Let K be point I translated by vector J. Point D is obtained by rotating point U by angle 5pi/12 about point Z. Let F be the vector from point U to point I. Point R is the translation of point K... | 0.7 | MATH |
[
{
"content": "Let CH = 12. Let W be the rotation of point C by angle 5pi/12 around point H. Line N passes through point H parallel to segment CW. Line U is the reflection of line N across point W. Point E is the midpoint of segment HC. Point T is the reflection of point W across line U. Point L is the reflectio... | 52.16 | MATH |
[
{
"content": "WE = 2. Let X be the rotation of point E by angle 3pi/4 around point W. Point S is obtained by rotating point X by angle 3pi/4 about point E. Let J be the reflection of point W across point E. Let Y be the line through points X and E. Let U be the line through point X perpendicular to line Y. Let ... | 2.16 | MATH |
[
{
"content": "AW = 7. Point M is obtained by rotating point A by angle 2pi/3 about point W. Point V is obtained by rotating point W by angle pi/12 about point M. Point E is the reflection of point W across point V. Let F be the circumcenter of triangle EMV. Let T be the incenter of triangle EMV. What is the mea... | 0.73 | MATH |
[
{
"content": "Let XD = 2. Point Z is the reflection of point X across point D. Point U is obtained by rotating point Z by angle 3pi/4 about point D. Let Y be the perpendicular bisector of segment DZ. Point H is the centroid of triangle XUZ. Point I is the reflection of point H across line Y. Let F be the incent... | 0.06 | MATH |
[
{
"content": "OU = 3. Let G be the rotation of point U by angle pi/4 around point O. Let Y be the incircle of triangle UGO. Point K is the incenter of triangle UGO. Let P be the inversion of point U in circle Y. What is the length of segment KP? Express your answer as a decimal number rounded to 2 decimal place... | 0.43 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.