MathNet 2009-part-02 — 175 problems (EN–VI) Question 39

Let $ABC$ be a triangle and let $P$ be an interior point such that $\angle BPC = 90^{\circ}$, $\angle BAP = \angle BCP$. Let $M, N$ be the mid-points of $AC, BC$ respectively. Suppose $BP = 2PM$. Prove that $A, P, N$ are collinear.