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X(6), X(53), X(216), X(1249)

midpoints of ABC

Ωa, Ωb, Ωc see Table 41 and CL052

K307 is the locus of poles of all pK having the same asymptotic directions as the McCay cubic i.e. having three real asymptotes perpendicular to the sidelines of the Morley triangle. For example, with the poles X(53), X(216) we obtain the McCay orthic cubic K049, K096 respectively.

The tangents at A, B, C to K307 concur at X(51), the centroid of the orthic triangle.

See also K080, the locus of pivots of all pK having the same asymptotic directions as the McCay cubic.

See "Asymptotic Directions of Pivotal Isocubics" in the downloads page.

K307 is also psK(X51, X2, X6) in Pseudo-Pivotal Cubics and Poristic Triangles.