Question 195
Let $ABCD E$ be a convex pentagon such that $BC = DE$. Assume there is a point $T$ inside $ABCDE$ with $TB = TD$, $TC = TE$ and $\angle TBA = \angle AET$. Let lines $CD$ and $CT$ intersect line $AB$ at points $P$ and $Q$, respectively, and let lines $CD$ and $DT$ intersect line $AE$ at points $R$ and $S$, respectively. Assume that points $P, B, A, Q$ and $R, E, A, S$ respectively, are collinear and occur on their lines in this order. Prove that the points $P, S, Q, R$ are concyclic.
(Slovakia)
(Slovakia)