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K411

X(3), X(32), X(15371), X(19597)

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

K411 is another example of cubic passing through the vertices A', B', C' of the ITB triangle. See also K410, K1098 and K003.

The conic inscribed in both triangles ABC and A'B'C' is the Brocard ellipse. See a generalization at K410.

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).