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X(6), X(37), X(570) extraversions of X(37) infinite points of pK(X39, X6) midpoints of the symmedians square roots of X(39) 

The locus of point P such that the center of the bicevian conic C(P, P*) lies on the line PP* is the Grebe cubic K102 (Francisco Javier García Capitán). The locus of this center is K437, a nodal cubic with node K. 
