RMO 2015 M5

Let $ABC$ be a right-angled triangle with $\angle B = 90^\circ$ and let $BD$ be the altitude from $B$ on to $AC$ . Draw $DE \perp AB$ and $DF \perp BC$ . Let $P, Q, R$ and $S$ be respectively the incentres of triangle $DF C, DBF, DEB$ and $DAE$ . Suppose $S, R, Q$ are collinear. Prove that $P, Q, R, D$ lie on a circle.