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X(2), X(4), X(193)

vertices of the orthic triangle

points at infinity of the Thomson cubic.

K181 is the isogonal transform of K167 = pK(X184, X6) and the isotomic transform of pK(X69, X2). It is a member of the class CL007 of cubics.

Its asymptotes are parallel to those of the Thomson and Lucas cubics.

It is tangent at A, B, C to the medians and at H to the Euler line.

It meets the circumcircle at the same points as the isogonal pK with pivot X(3060). (green curve)

K181 is the locus of point P such that the trilinear polar of P is perpendicular to the line PH. See CL040 for a generalization.