Question 24
Let $ABC$ be an acute triangle such that angle $B$ measures $60^\circ$. The circle of diameter $AC$ cuts the interior bisectors of the angles $A$ and $C$ at the points $M$ and $N$, respectively ($M \neq A$, $N \neq C$). The interior bisector of angle $B$ cuts $MN$ and $AC$ at points $R$ and $S$, respectively. Prove that $BR \le RS$.