Question 141
Given an isosceles triangle $ABC$ with $AB = AC$. Let a moving point $D$ satisfy $AD \parallel BC$ and $DB \gt DC$. Let a moving point $E$ be on the arc $\widearc{BC}$ of the circumcircle of $\triangle ABC$ that does not contain $A$, such that $EB \lt EC$. Let $F$ be a point on the extension of $BC$ such that $\angle DFE = \angle ADE$. The extension of $FD$ intersects the extension of $BA$ at point $X$, and the extension of $FD$ intersects the extension of $CA$ at point $Y$.
Prove that $\angle XEY$ is constant.
Prove that $\angle XEY$ is constant.