Question 28
Let $ABC$ be a triangle, obtuse at $C$, such that $2\angle BAC = \angle ABC$. Let $P$ be a point on side $AB$ such that $BP = 2BC$. Let $M$ be the midpoint of $AB$ ($M$ lies between $P$ and $B$). Prove that the perpendicular to side $AC$ drawn through $M$ meets $PC$ at its midpoint.