Question 135
Let $\triangle ABC$ be a triangle and let $D$ be a point in its interior. Construct a circle $\omega_1$ passing through $B$ and $D$ and a circle $\omega_2$ passing through $C$ and $D$ such that the point of intersection of $\omega_1$ and $\omega_2$ other than $D$ lies on line $AD$. Denote by $E$ and $F$ the points where $\omega_1$ and $\omega_2$ intersect side $BC$, respectively, and by $X$ and $Y$ the intersections of lines $DF$, $AB$ and $DE$, $AC$, respectively. Prove that $XY \parallel BC$.