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X(1), X(4), X(1490)

foci of the circum-conic with center X(1), perspector X(9)

antipodes of A, B, C on (O)

vertices of the cevian triangle of X(329)

K712 is a circum-cubic that passes through the foci of the circum-conic (C) with center X(1), perspector X(9).

K712 meets :

• the line at infinity at the same points as K692 = pK(X6, X8) or pK(X9, X3436),

• the circum-conic (C) at the same points as pK(X9, X78).

• the circumcircle at the same points as the Darboux cubic K004 or pK(X1033, X4).