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X(4), X(6), X(32), X(218), X(1992)

vertices of the pedal triangle of K

projections of K on the altitudes

K055 is a generalized Lemoine cubic as seen in the FG paper. See also Table 64.

It is a nodal cubic with node K and the nodal tangents are parallel to the asymptotes of the Jerabek hyperbola.

It has the same asymptotic directions as K169 = pK(X6, X69) and K1365 = pK(X2, X315).

It meets the circumcircle at the same points as the isogonal pK whose pivot is the intersection X(22253) of the lines X(3)X(194) and X(6)X(538).

The isogonal transform of K055 is K657.