Question 78
Let $ABC$ be an acute triangle with $AB = 11$, $AC = 10$, and denote the orthocenter by $H$ and the midpoint of $BC$ by $M$. Point $P$ in triangle $ABC$ lies on the circumcircle of triangle $BHC$ and satisfies $\angle ABP = \angle CPM$, $PM = 3$. Find the length of $BC$.