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Found problems: 1

2018 Singapore MO Open, 2
Tags: smo , geometry
Let O be a point inside triangle ABC such that $\angle BOC$ is $90^\circ$ and $\angle BAO = \angle BCO$. Prove that $\angle OMN$ is $90$ degrees, where $M$ and $N$ are the midpoints of $\overline{AC}$ and $\overline{BC}$, respectively.