Question 33
Let $\triangle ABC$ be an acute angled triangle with $AB \lt AC$ and $O$ be the center of its circumcircle $\omega$. Let $D$ be a point on the segment $BC$ such that $\angle BAD = \angle CAO$. Let $E$ be the second point of intersection of $\omega$ and the line $AD$. If $M, N$ and $P$ are the midpoints of the line segment $BE, OD$ and $AC$, respectively, show that the points $M, N$ and $P$ are collinear.
