ELMO SL 2014 G9

Let $P$ be a point inside a triangle $ABC$ such that $\angle PAC= \angle PCB$ . Let the projections of $P$ onto $BC$ , $CA$ , and $AB$ be $X,Y,Z$ respectively. Let $O$ be the circumcenter of $\triangle XYZ$ , $H$ be the foot of the altitude from $B$ to $AC$ , $N$ be the midpoint of $AC$ , and $T$ be the point such that $TYPO$ is a parallelogram. Show that $\triangle THN$ is similar to $\triangle PBC$ .

Proposed by Sammy Luo