RO-NMO 2019 Problem 91

Let be a point $P$ in the interior of a triangle $ABC$ such that $BP=AC, M$ be the middlepoint of the segment $AP, R$ be the middlepoint of $BC$ and $E$ be the intersection of $BP$ with $AC.$ Prove that the bisector of $\angle BEA$ is perpendicular on $MR$