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too complicated to be written here. Click on the link to download a text file. 

X(250), X(523) vertices of the cevian triangle of X(264) 

K556 is an axial cubic symmetric about the Euler line. K556 is the pseudopivotal cubic psK(X4, X264, X523). See PseudoPivotal Cubics and Poristic Triangles. The tangents at A, B, C are the symmedians. 
