KöMaL 2012 B4477

In an acute triangle ABC , $\alpha$<$\beta$ (with conventional notations). Let $R$and $P$ be the feet of the altitudes drawn from vertices $A$ and $C$, respectively. Let $Q$ denote a point of line $AB$, different from $P$, such that $AP^. BQ$=$AQ^. BP$. Prove that line $RB$ bisects the angle PRQ .