CN-LEAGUE 2005 Problem 1

In $\triangle ABC$ , $AB>AC$ , $l$ is a tangent line of the circumscribed circle of $\triangle ABC$ , passing through $A$ . The circle, centered at $A$ with radius $AC$ , intersects $AB$ at $D$ , and line $l$ at $E, F$ . Prove that lines $DE, DF$ pass through the incenter and an excenter of $\triangle ABC$ respectively.