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K926

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X(4), X(40), X(56), X(280), X(505)

vertices of the extouch triangle = pedal triangle of X(40) = cevian triangle of X(8)

antipodes of A, B, C on (O)

projections of X(40) on the altitudes

infinite points of pK(X6, X692)

Geometric properties :

K926 is the Lemoine generalized cubic K(X40) hence it is a nodal cubic with node X(40), the nodal tangents being perpendicular.

K926 is also psK(X198, X8, X4) in Pseudo-Pivotal Cubics and Poristic Triangles.

K926 is the isogonal transform of K654.

K926 and K654 meet at A, B, C and three pairs of (not always real) points lying on the internal bisectors of ABC. See the analogous cubics K360 and K259.