VWO 2007 Problem 2

Given is a half circle with midpoint $O$ and diameter $AB$ . Let $Z$ be a random point inside the half circle, and let $X$ be the intersection of $OZ$ and the half circle, and $Y$ the intersection of $AZ$ and the half circle.

If $P$ is the intersection of $BY$ with the tangent line in $X$ to the half circle, show that $PZ \perp BX$ .