Question 88
Let $ABC$ be an acute-angled scalene triangle. The internal angle bisector of vertex $A$ intersects the opposite side $BC$ at $E$ and the minor arc $BC$ of the circumcircle of $\triangle ABC$ at $M$. Suppose $D \neq M$ is a point on the minor arc $BC$ such that $ED = EM$. Also, let $P$ be a point on the line segment $AD$ such that $\angle ABP = \angle ACP \neq 0$. If $O$ is the circumcenter of $\triangle ABC$, prove that $OP \perp AM$.