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X(4), X(1656), X(1657), X(14841)

Let P be a point and A'B'C' its cevian triangle. SaSbSc is the triangle formed by the reflections of P in the sidelines of ABC. Ra is the reflection of A' in the parallel at P to BC, Rb, Rc similarly. The triangles RaRbRc and SaSbSc are perspective if and only if P lies on K194 (together with the line at infinity).

K194 is pK(X14840, X14841).

K194 belongs to the pencil of cubics generated by the McCay cubic K003, the Lucas cubic K007 and Kn = K060. Hence the tangents at A, B, C are the altitudes and the common polar conic of H in all cubics of the pencil is the Jerabek hyperbola. The pole lies on the circum-conic through G and K, the pivot lies on the Jerabek hyperbola, the isoconjugate of the pivot is H.

The pencil also contains the cubics : pK(X25, X6), pK(X37, X72), pK(X42, X71), pK(X1400, X73), pK(X1976, X248), pK(X1880, X65), pK(X2165, X68) and many others. See K195 for example and also the orange cells in CL024.