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X(2), X(4), X(6), X(22), X(69), X(76), X(1670), X(1671)

vertices of antimedial triangle

cevians of X(76)

points at infinity of the Grebe cubic

The parallels to the symmedians drawn through a point P meet the sidelines of ABC at Pa, Pb, Pc. ABC and PaPbPc are perspective if and only if P lies on pK(X39, X69) = K140. The locus of the perspector is pK(X2, X76) = K141. See Special isocubics ยง3.2.4.

The tangents at A, B, C are the symmedians. The asymptotes are parallel to those of the Grebe cubic i.e. pK(X6, X6) = K102.

The isogonal transform of K141 is K177. Its complement is K836. See also K002, property 10.

K141 is a member of the class CL043 : it meets the circumcircle at A, B, C and three other points where the tangents are concurrent.