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K668

too complicated to be written here. Click on the link to download a text file.

X(1), X(5), X(30), X(54), X(74), X(186), X(265)

excenters

A', B', C' : vertices of the cevian triangle of X(265)

Q1, Q2 : intersections of the circumcircle and the perpendicular bisector of OH

common points of the line X(3)X(265) and the rectangular circum-hyperbola passing through X(186). These points are isogonal conjugates and lie on the McCay cubic K003

K668 is an isogonal pivotal cubic related with the stelloid K669.

These two cubics have six common points on the circumcircle (O) and three common points on the line (L) = X(3)X(265). They generate a pencil of cubics containing :

• the decomposed cubic into (O) and (L),

• two psKs namely psK(X265, X328 x X3580, X68) and psK(X74 x X1989, X74 x X328, X64),

• another complicated nK.