Inscribed quadrilateral and equal angles

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Let $ABCD$ is a quadrilateral inscribed in a circle with center $O$ and $P$ is the intersection point of the diagonals.
Prove that if $M$ is the middle of the side $AB$ and $N$ is the middle of the side $CD$ then $\angle OMP = \angle ONP$.

(Оффтоп)

This problem have solution in 3-4 rows. It is not a difficult problem but I think it is funny.