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X(4), X(3090), X(3529), X(14843)

P1 = X(3529), P2= X(3090) on the Euler line

X(14843) on the Jerabek hyperbola

Let P be a point, A'B'C' its cevian triangle and PaPbPc its pedal triangle. Ra is the reflection of A' in the parallel at P to BC, Rb, Rc similarly. The triangles RaRbRc and PaPbPc are perspective if and only if P lies on K195 (together with the line at infinity).

K195 is pK(X14842, X14843).

K195 belongs to the pencil of cubics generated by the McCay cubic K003, the Lucas cubic K007 and Kn = K060. See K194 and also the orange cells in CL024.