Problem

Source: - All-Russian MO 2003 Regional (R4) 9.6

Tags: geometry, Concyclic, incenter



Let $I$ be the intersection point of the bisectors of triangle $ABC$. Let us denote by $A', B', C'$ the points symmetrical to $I$ wrt the sides triangle $ABC$. Prove that if a circle circumscribes around triangle $A'B'C'$ passes through vertex $B$, then $\angle ABC = 60^o$.