Question 36
In an isosceles triangle $ABC$ ($BC = BA$), point $P$ is arbitrarily chosen on the altitude from vertex $B$. Suppose that the circumcircle of $BAP$ intersects $AC$ for the second time at point $M$. Let $N$ be the reflection of $M$ with respect to the midpoint of $AC$. $NP$ intersects the circumcircle of $BAP$ at $X$ ($X \neq P$), and $AB$ intersects the circumcircle of $NAP$ at $Y$ ($Y \neq A$). The tangent to the circumcircle of $NAP$ at $A$ intersects $BP$ at $Z$. Prove that $CZ$ is tangent to the circumcircle of $XYP$.