IR-TST 2008 Problem 2

Suppose that $I$ is incenter of triangle $ABC$ and $l'$ is a line tangent to the incircle. Let $l$ be another line such that intersects $AB,AC,BC$ respectively at $C',B',A'$ . We draw a tangent from $A'$ to the incircle other than $BC$ , and this line intersects with $l'$ at $A_1$ . $B_1,C_1$ are similarly defined. Prove that $AA_1,BB_1,CC_1$ are concurrent.