1. In $\triangle A B C$, $A C>A B, P$ is the intersection of the perpendicular bisector of $B C$ and the internal angle bisector of $\angle A$, draw $P X \perp A B$, intersecting the extension of $A B$ at point $X, P Y \perp A C$ intersecting $A C$ at point $Y, Z$ is the intersection of $X Y$ and $B C$. Find the value of $\frac{B Z}{Z C}$.