Trilinears 1/(b + c - a) : 1/(c + a - b) : 1/(a + b - c)
= tan(A/2) : tan(B/2) : tan(C/2)
Barycentrics a/(b + c - a) : b/(c + a - b) : c/(a + b - c)
X(57) is the perspector of the intouch triangle and excentral triangle.
X(57) lies on these lines:
1,3 2,7 4,84 6,222 10,388 19,196 20,938 27,273 28,34 31,105 33,103 38,612 42,1002 43,181 72,474 73,386 77,81 78,404 79,90 85,274 88,651 92,653 164,177 169,277 173,174 200,518 201,975 234,362 239,330 255,580 279,479 345,728 497,516 499,920 649,1024 658,673 748,896 758,997 955,991 957,995 959,1042 961,1106 978,1046 1020,1086
X(57) is the {X(2),X(7)}-harmonic conjugate of X(226).
X(57) = reflection of X(I) in X(J) for these (I,J): (1,999), (200,1376)
X(57) = isogonal conjugate of X(9)
X(57) = isotomic conjugate of X(312)
X(57) = inverse-in-Bevan-circle of X(1155)
X(57) = complement of X(329)
X(57) = X(I)-Ceva conjugate of X(J) for these (I,J):
(2,223), (7,1), (27,278), (81,222), (85,77), (273,34), (279,269)
X(57) = cevapoint of X(I) and X(J) for these (I,J): (6,56), (19,208)
X(57) = X(I)-cross conjugate of X(J) for these (I,J): (6,1), (19,84), (56,269), (65,7)
X(57) = crosspoint of X(I) and X(J) for these (I,J): (2,189), (7,279), (27,81), (85,273)
X(57) = crosssum of X(I) and X(J) for these (I,J): (1,165), (6,198), (31,205), (37,71), (41,212), (55,220), (210,1334)
X(57) = crossdifference of any two points on line X(650)X(663)
X(57) = X(I)-Hirst inverse of X(J) for these (I,J): (1,241), (7,1447), (56,1429), (105,1462), (910,1419)
X(57) = X(I)-aleph conjugate of X(J) for these (I,J):
(2,40), (7,57), (57,978), (174,1), (366,165), (507,503), (508,9), (509,43)
X(57) = X(I)-beth conjugate of X(J) for these (I,J):
(2,2), (81,57), (88,57), (100,57), (110,31), (162,57), (190,57), (333,63), (648,92), (651,57), (653,57), (655,57), (658,57), (660,57), (662,57), (673,57), (771,57), (799,57), (823,57), (897,57)
, select the center name from the list and, then, click on the vertices A, B and C successively.