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X(3), X(32)

vertices of A'B'C', the only triply bilogic triangle inscribed in the circumcircle (Jean-Pierre Ehrmann, Hyacinthos #14350).

K411 is another example of cubic passing through the points A', B', C'. See also K410 and K003.

The conic inscribed in both triangles ABC and A'B'C' is the Brocard ellipse.

The polar conic of O is remarkable since it contains a large number of ETC centers namely : X(3), X(25), X(32), X(98), X(184), X(228), X(878), X(1402), X(1410), X(1799), X(2200), X(2351), X(2353).