SHARYGIN 2021 Problem 96

The diagonals of trapezoid $ABCD$ ( $BC\parallel AD$ ) meet at point $O$ . Points $M$ and $N$ lie on the segments $BC$ and $AD$ respectively. The tangent to the circle $AMC$ at $C$ meets the ray $NB$ at point $P$ ; the tangent to the circle $BND$ at $D$ meets the ray $MA$ at point $R$ . Prove that $\angle BOP =\angle AOR$ .