Ga, Gb, Gc :vertices of the antimedial triangle
Let P be a point and PaPbPc its cevian triangle. The antiparallels through Pa, Pb, Pc to the sidelines of ABC concur if and only if P lies on K211. The locus of the point of concurrence is K212.
K211 is a nK with pole H and root X(264), the isotomic conjugate of O.
The tangents at A, B, C are the sidelines of the tangential triangle. They meet the cubic again on the trilinear polar of X(250), the isogonal conjugate of the Jerabek center X(125).
The complement of K211 is a cubic psK(X647, X2, ?).
Other locus properties :