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X(4), X(5), X(52), X(61), X(62), X(143), X(2912), X(2913), X(3518)

vertices of the orthic triangle HaHbHc

K416 = pK(X14577, X4) is the Napoleon cubic for the orthic triangle HaHbHc. Hence, it is the locus of M such that :

– X(143) (the nine point center of the orthic triangle), M and the isogonal conjugate of M with respect to the orthic triangle are collinear,

– H, M and the isoconjugate of M in the isoconjugation swapping H and X(143) are collinear.