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X(3), X(4), X(20), X(72), X(185), X(1071), X(5562)

X(5562) = reflection of X(185) about X(3)

The Lucas cubic K007 is the locus of point P such that the cevian triangles of P and its isotomic conjugate P' are orthologic.

The locus of the centers of orthology O1, O2 is K401. These points are symmetric about O hence K401 is a central cubic.

It has three real asymptotes which are the cevian lines of O.

The inflexional tangent at O passes through X(69), the pivot of K007.

K401 contains the vertices of the cevian triangle of X(69) – with tangents passing through L = X(20) – and their reflections in O. These latter points lie on the altitudes which are the tangents at these points. The six points lie on the inconic with center O, perspector X(69).