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K415

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X(4), X(5), X(24), X(52), X(371), X(372), X(2904)

vertices of the orthic triangle HaHbHc

vertices of the orthic triangle of the orthic triangle

K415 = pK(X14576, X4) is the Orthocubic for the orthic triangle HaHbHc. Hence, it is the locus of M such that :

– X(52) (the orthocenter of the orthic triangle), M and the isogonal conjugate of M with respect to the orthic triangle are collinear,

– X(5) (the circumcenter of the orthic triangle), M and the isogonal conjugate of M with respect to the orthic triangle of the orthic triangle are collinear,

– H, M and the isoconjugate of M in the isoconjugation swapping H and X(52) are collinear.

Hence K415 is an isogonal pK in two different triangles like K006 and K414. See the related K627.

K415 meets the Orthocubic K006 at A, B, C, H, Ha, Hb, Hc, X(371), X(372).