CGMO 2017 Problem 7

This is a very classical problem. Let the $ABCD$ be a cyclic quadrilateral with circumcircle $\omega_1$ .Lines $AC$ and $BD$ intersect at point $E$ ,and lines $AD$ , $BC$ intersect at point $F$ .Circle $\omega_2$ is tangent to segments $EB,EC$ at points $M,N$ respectively,and intersects with circle $\omega_1$ at points $Q,R$ .Lines $BC,AD$ intersect line $MN$ at $S,T$ respectively.Show that $Q,R,S,T$ are concyclic.

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