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X(2), X(3), X(6), X(67), X(111), X(187), X(468), X(524), X(1560)

complement of X(67)

vertices of medial triangle

E = X(2482) = (b^2 + c^2 - 2a^2)^2 : : , complement of X(671), antipode of X(115) on the Steiner in-ellipse

K043 is the only circular pK with pivot G = X(2). Its pole is X(187), the Schoute center (inverse of K in the circumcircle).

The singular focus is the midpoint of X(3)X(111).

K043 is :

• the complement of the Droussent cubic which is pK(G, X316)
• the isogonal transform of K273
• the inversive image of K108 in the circumcircle. See also Inverses of Isocubics.

More generally, given a circum-conic (C) with perspector W, the locus of point M such that the trilinear polar and the polar line in (C) of M are parallel is the pK with pole W and pivot G. It is the complement of the isotomic pK with pole W' = anticomplement of W.

For example, with W = X(6), (C) is the circumcircle and the cubic is the Thomson cubic, complement of the Lucas cubic.

See also K007, property 8 and K002, property 12.