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X(1), X(6), X(43), X(292), X(727), X(3009), X(20663), X(20671), X(21760), X(51864)

vertices of the cevian triangle of X(6)

points on (O) and on the Lemoine axis

P1 on the lines {6, 2109}, {292, 3009}, {727, 21760}

Geometric properties :

The cevian triangle of P is perspective to the circumcevian triangle of X(3009) if and only if P lies on K1415.