OSN 2011 Problem 8

Given a triangle $ABC$ . Its incircle is tangent to $BC, CA, AB$ at $D, E, F$ respectively. Let $K, L$ be points on $CA, AB$ respectively such that $K \neq A \neq L, \angle EDK = \angle ADE, \angle FDL = \angle ADF$ . Prove that the circumcircle of $AKL$ is tangent to the incircle of $ABC$ .