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X(4), X(110), X(523) vertices of the cevian triangle of X(99) 

K568 is a circular cubic with focus X(399). See PseudoPivotal Cubics and Poristic Triangles. It is the isogonal transform of K567. These two cubics belong to a same pencil of circular cubics generated by pK(X6, X523) and the union of the line at infinity and the circumconic with perspector X(187). See also Table 46. 
