CONO-SUR 2003 Problem 3

Let $ABC$ be an acute triangle such that $\angle{B}=60$ . The circle with diameter $AC$ intersects the internal angle bisectors of $A$ and $C$ at the points $M$ and $N$ , respectively $(M\neq{A},$ $N\neq{C})$ . The internal bisector of $\angle{B}$ intersects $MN$ and $AC$ at the points $R$ and $S$ , respectively. Prove that $BR\leq{RS}$ .