BG-MO 1994 Problem 4

Let $ABC$ be a triangle with incenter $I$ , and let the tangency points of its incircle with its sides $AB$ , $BC$ , $CA$ be $C'$ , $A'$ and $B'$ respectively. Prove that the circumcenters of $AIA'$ , $BIB'$ , and $CIC'$ are collinear.