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X(4), X(521) 

K247 is a member of the class CL024 of cubics. Denote by A', B', C' the "second" common points of the lines AP, BP, CP and the Feuerbach hyperbola. A'B'C' and the pedal triangle of P are perspective if and only if P lies on K247, together with the circumcircle and the line at infinity. K247 is the isogonal transform of pK(X1415, X3). 
