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K693

a^2 x (y - z) (c^4 y + b^4 z) = 0

to compare with the equation of K444 :

a^2 x (y + z) (c^4 y - b^4 z) = 0

X(2), X(184), X(3168)

A'B'C' : cevian triangleof K

K693 is another (simple) example of cubic meeting the circumcircle at six points with concurrent tangent, here at X(6). See the related K444, K579, K694.

See Cubics Related to Coaxial Circles §10.4 and Circumcubics meeting the Circumcircle at six points with concurring tangents.

See also Pseudo-Pivotal Cubics and Poristic Triangles.

The isogonal transform of K693 is psK(X2, X2, X6).