Question 168
Let $ABC$ be an acute triangle. Let $H$ be the foot of the altitude from $C$ onto $AB$. Suppose that $|AH| = 3|BH|$. Let $M$ and $N$ be the midpoints of $AB$ and $AC$ respectively. Let $P$ be a point such that $|NP| = |NC|$ and $|CP| = |CB|$ and such that $B$ and $P$ lie on different sides of line $AC$.
Prove that $\angle APM = \angle PBA$.
Prove that $\angle APM = \angle PBA$.