Question 17
Let $ABCD$ be a cyclic quadrilateral with circumcircle $\omega$, and let $E$ be the intersection of the diagonals $AC$ and $BD$. A line passing through $E$ intersects the lines $AB$, $BC$ at $P, Q$, respectively. Let $R$ ($R \neq D$) be the intersection point of $\omega$ and the circle that passes through $D, E$ and is tangent to the line $PQ$ at $E$. Prove that $B, P, Q, R$ are concyclic.
(Proposed by B. Khoroldagva)
(Proposed by B. Khoroldagva)