Question 43
Let $ABC$ be a triangle. Let $D$ and $E$ be respectively points on the segments $AB$ and $AC$, and such that $DE \parallel BC$. Let $M$ be the midpoint of $BC$. Let $P$ be a point such that $DB = DP$, $EC = EP$ and such that the open segments (segments excluding the endpoints) $AP$ and $BC$ intersect. Suppose $\angle BPD = \angle CME$. Show that $\angle CPE = \angle BMD$.