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K452
equK452

X(2), X(13), X(14), X(468), X(524), X(1992)

vertices A', B', C' of the pedal triangle of G

Q = X(9084), on the circumcircle

S = X(15303) = X(13)X(14) /\ X(468)X(524) /\ X(1992)X(9084)

X = X(15304) = X(2)X(1296) /\ X(126)X(524), on the real asymptote

For any point P on K295, the orthopivotal cubic O(P) meets the sidelines of ABC at three points which are the vertices of the pedal triangle of a point on the Kiepert hyperbola.

This is the case of K452 and K059.

K452 is a circular cubic with singular focus F = X(9172), the midpoint of X(2)-X(111) or the reflection of X(126) about X(2).