+182 Let H be the orthocenter of acute triangle ABC, and let M be the midpoint of \overline{AC}. Ray $\overrightarrow{MH}$ intersects the circumcircle of triangle $ABC$ at $P.$ If $BC < AB,$ $\angle ABP = 60^\circ,$ $MH = 14,$ and $HP = 3,$ then find length $BC.$
Note: The orthocenter of a triangle is the point where the altitudes of the triangle meet.
