MathNet 2009-part-03 — 175 problems (EN–VI) Question 87

Let $ABCDE$ be a convex pentagon with $AB + CD = BC + DE$, and $k$ a circle centered on side $AE$, tangent to sides $AB$, $BC$, $CD$ and $DE$ at points $P$, $Q$, $R$ and $S$ respectively. Prove that lines $PS$ and $AE$ are parallel.