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K612

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X(2), X(3), X(5), X(6), X(216), X(343), X(2165)

midpoints of ABC

infinite points of pK(X6, X1993)

points of pK(X6, X343) on (O)

The vertices of the Johnson triangle are the reflections of O in the sidelines of ABC or the reflections of A, B, C about X(5).

K612 is the locus of M such that the anticevian triangle of M and the Johnson triangle are perspective at P. (C├ęsar Lozada, ADGEOM #1168).

The locus of P is K044.

If "anticevian" is replaced by "cevian" we obtain K674.

 

K612 is the isotomic transform of pK(X276, X276), a member of CL007.

It is also the complement of K045 = pK(X2, X264).