KöMaL 2015 B4713

A circle passing through vertices $B$ and $C$ of triangle $ABC$ intersects side $AB$ at $D$ , and side $AC$ at $E$ . The intersection of lines $CD$ and $BE$ is $O$ . Let $M$ denote the centre of the inscribed circle of triangle $ADE$ , and let $N$ denote the centre of the inscribed circle of triangle $ODE$ . Prove that line $MN$ bisects the smaller arc $DE$ .