X(1), X(10), X(145), X(2136)
vertices of the cevian triangle of X(145)
K372 is another example of pK intersecting the isoconjugate (C) of the line at infinity at A, B, C and three other points forming an equilateral triangle T. Compare K372 and K371.
Its pole is X(37), center of the inconic with perspector I, and its pivot is X(145), the anticomplement of the Nagel point X(8).
The isopivot P* is a(b+c)/(b+c-3a) : : , on the line IX(2136)
(C) is the circum-conic with center X(10), perspector X(37) passing through X(80), X(100), X(291), X(668), X(1018), X(1783).
The circumcircle (T) of T is centered at I and has radius twice the inradius. It contains X(80). T is the homothetic of the circumnormal triangle (vertices on the McCay cubic) at the point X(36), the inverse of I in the circumcircle. Note that (T) and the circumcircle are homothetic at X(35) and X(36).
The third point on AX(1) is b+c:-3b:-3c and the third point on AX(10) is -3a:a+c:a+b, the other points similarly.