Question 2
Consider an arbitrary triangle $ABC$ with incenter $I$, and let $I_a$, $I_b$, and $I_c$ be the excenters of triangle $ABC$ opposite to vertices $A$, $B$, and $C$, respectively, tangent to sides $BC$, $CA$, and $AB$. Let $E$, $F$, and $G$ be the points of tangency of the incircle with the sides $BC$, $CA$, and $AB$, respectively.
Prove that the circumcircles of triangles $IEI_a$, $IFI_b$, and $IGI_c$ intersect in a second common point different from $I$.
Petru Braica
Prove that the circumcircles of triangles $IEI_a$, $IFI_b$, and $IGI_c$ intersect in a second common point different from $I$.
Petru Braica