Given triangle $ ABC$. Points $ M$, $ N$ are the projections of $ B$ and $ C$ to the bisectors of angles $ C$ and $ B$ respectively. Prove that line $ MN$ intersects sides $ AC$ and $ AB$ in their points of contact with the incircle of $ ABC$.
Problem
Source: I.F.Sharygin contest 2009 - Correspondence round - Problem 7
Tags: geometry, geometry proposed