MathNet 2018-part-05 — 181 problems (EN–VI) Question 106

Let $O$ be a point inside a triangle $ABC$ such that $\angle BOC = 90^\circ$ and $\angle BAO = \angle BCO$. Prove that $\angle OMN = 90^\circ$, where $M$, $N$ are the midpoints of $AC$ and $BC$ respectively.