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K690

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X(4), X(68), X(485), X(486), X(637), X(638), X(14784), X(14785)

X(14784), X(14785) on the Euler line

points at infinity of the Orthocubic

K690 is a member of the pencil of cubics generated by the Orthocubic K006 and the cubic decomposed into the line at infinity and the Kiepert hyperbola. It is the only other pK of the pencil apart K006. Other members are K120, K122.

K690 is also a member of the pencil of cubics generated by the McCay cubic K003 and the Lucas cubic K007. See CL024.

The tangents at A, B, C are the altitudes and the polar conic of H is the Jerabek hyperbola.

It is an example of pK having asymptotes parallel to three concurring Simson lines. See the papers Asymptotic Directions of Pivotal Isocubics and The Cevian Simson Transformation.

Its isogonal transform is pK(X571, X3). See K920.