CMO 2001 Problem 3

Let $ABC$ be a triangle with $AC > AB$ . Let $P$ be the intersection point of the perpendicular bisector of $BC$ and the internal angle bisector of $\angle{A}$ . Construct points $X$ on $AB$ (extended) and $Y$ on $AC$ such that $PX$ is perpendicular to $AB$ and $PY$ is perpendicular to $AC$ . Let $Z$ be the intersection point of $XY$ and $BC$ . Determine the value of $\frac{BZ}{ZC}$ .