Dear Ivan and François! I found the proof. Consider projective map transforming the inconic to the circle and the concurrence point to its center. It is easy
Variation: Let ABC be a triangle and F1,F2,F3 the ex-Feuerbach points of the triangles HBC,HCA,HAB corrsponding to angles (HBC),(HCA),(HAB), resp. Let (K1) be
Dear François, I do not consider triangles, I consider 2k+1 - gons with k > 1, so the smallest case is pentagon. In the case of a triangle, indeed the locus
Dear Francois! If we look at the configuration of a triangle ABC and its contact triangle A'B'C', then we know lines AA', BB', CC' are on the Gergonne point of