Inscribed quadrilateral and concyclic points

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Let $ABCD$ is an inscribed quadrilateral in the circle $k$ and $E$ is the intersection point of $AD$ and $BC$. $EK$ and $EL$ are the tangets from $E$ to $k$. $KL$ intersects $AD$ and $BC$ at the points $P$ and $Q$. $M$ and $N$ are the middles of the sides $AD$ and $BC$. Prove that $M$, $N$, $P$, $Q$ are concyclic.