Question 98
Let $\triangle ABC$ be an isosceles triangle with $|AB| = |AC|$. Let $D$ be an arbitrary point on segment $BC$. Let $X$ and $Y$ be points on $AB$ and $AC$, respectively, such that $XY \nparallel BC$ and $XY$ passes through the midpoint of $AD$. Prove that if the circumcenter of $\triangle ABC$ lies on $\odot(AXY)$ then the quadrilateral $AYDX$ is a parallelogram.