JBMO 2009 Problem 1

Let $ABCDE$ be a convex pentagon such that $AB+CD=BC+DE$ and $k$ a circle with center on side $AE$ that touches the sides $AB$ , $BC$ , $CD$ and $DE$ at points $P$ , $Q$ , $R$ and $S$ (different from vertices of the pentagon) respectively. Prove that lines $PS$ and $AE$ are parallel.