IR-TST 2009 Problem 1

Let $ABC$ be a triangle and $A'$ , $B'$ and $C'$ lie on $BC$ , $CA$ and $AB$ respectively such that the incenter of $A'B'C'$ and $ABC$ are coincide and the inradius of $A'B'C'$ is half of inradius of $ABC$ . Prove that $ABC$ is equilateral .