1831. ConConic Triangles

 Let P be a point and A1B1C1 cevian triangle of P.

ta= tangent to circumcircle of A1B1C1 at A1. Define tb, tc cyclically.
Let A2B2C2 triangle bounded by lines ta, tb, tc.

*A,B,C, A2,B2,C2 lie on same conic.
** For P=X(2), Center of the conic is X(15449)-CENTER OF THE X(2)-ALTINTAS HYPERBOLA.
*** Which is the center of the conic for some triangle centers?