Incenters often Vex 😦

Let $ABC$ be a right triangle right angled at $B$ . Draw $BD \perp AC$ , $DE \perp AB$ and $DF \perp BC$ . Let $P,Q,R$ and $S$ be the incentres of triangle $CDF , BDF , BDE$ and $ADE$ , respectively. It is given that $S, R$ and $Q$ are collinear and also, $RQ = 5 , QP = 9 DP = 12$ and $RD = 10$ . Find the numerical value of the product $PR \times DQ$ .