IR-MO 2002 Problem 19

$I$ is incenter of triangle $ABC$ . Incircle of $ABC$ touches $AB,AC$ at $X,Y$ . $XI$ intersects incircle at $M$ . Let $CM\cap AB=X'$ . $L$ is a point on the segment $X'C$ that $X'L=CM$ . Prove that $A,L,I$ are collinear iff $AB=AC$ .