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X(2), X(6), X(1992)

projections of K on the sidelines of ABC

their reflections in K

points at infinity of the Thomson cubic

common points of the circumcircle and pK(X6, X1992)

foci of the K-ellipse (inellipse with center K when the triangle ABC is acute angle)

TC(X6) is a member of the class CL040 of Thomson centroidal cubics.

It is the locus of point M such that the trilinear polar of M is perpendicular to the line KM.

K314 is a central cubic with three real asymptotes concurring at K and parallel to those of the Thomson cubic. The tangent at K is the Brocard line.

K314 is spK(X2, X6) in CL055.

The isogonal transform of K314 is K1093.