KMO 2010 Problem 3

Let $I$ be the incenter of triangle $ABC$ . The incircle touches $BC, CA, AB$ at points $P, Q, R$ . A circle passing through $B , C$ is tangent to the circle $I$ at point $X$ , a circle passing through $C , A$ is tangent to the circle $I$ at point $Y$ , and a circle passing through $A , B$ is tangent to the circle $I$ at point $Z$ , respectively. Prove that three lines $PX, QY, RZ$ are concurrent.