CN-TST 2018 Problem 3

Circle $\omega$ is tangent to sides $AB$ , $AC$ of triangle $ABC$ at $D$ , $E$ respectively, such that $D\neq B$ , $E\neq C$ and $BD+CE<BC$ . $F$ , $G$ lies on $BC$ such that $BF=BD$ , $CG=CE$ . Let $DG$ and $EF$ meet at $K$ . $L$ lies on minor arc $DE$ of $\omega$ , such that the tangent of $L$ to $\omega$ is parallel to $BC$ . Prove that the incenter of $\triangle ABC$ lies on $KL$ .