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X(4), X(525) 

K245 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 Kiepert hyperbola. A'B'C' and the pedal triangle of P are perspective if and only if P lies on K245, together with the circumcircle and the line at infinity. K245 is the isogonal transform of pK(X1576, X3) and the isotomic transform of pK(X523, X69). 
