MYTS 2019 - Grade 9 - Round 2 Question 3

An acute triangle $ABC$ is inscribed in circle $(O)$. Choose $D$ on the minor arc $BC$, distinct from $B,C$. Draw $DX\perp BC$ and $DY\perp AC$. Let $M,N$ be the midpoints of $AB,XY$, respectively. Prove that $\angle DNM=90^\circ$.