IR-TST 2007 Problem 6

Let $\omega$ be incircle of $ABC$ . $P$ and $Q$ are on $AB$ and $AC$ , such that $PQ$ is parallel to $BC$ and is tangent to $\omega$ . $AB,AC$ touch $\omega$ at $F,E$ . Prove that if $M$ is midpoint of $PQ$ , and $T$ is intersection point of $EF$ and $BC$ , then $TM$ is tangent to $\omega$ . By Ali Khezeli