Question 74
Points $A, B, C, D$ lie on a circle $\omega$ and form a convex quadrilateral $ABCD$. Lines $AB$ and $CD$ meet at $E$, with $A$ between $B$ and $E$; lines $BD$ and $AC$ meet at $F$. Let $X$ be the point on $\omega$ other than $D$ such that $DX$ is parallel to $EF$. Let $Y$ be the reflection of $D$ in the line $EF$, and suppose that $Y$ lies inside $\omega$. Prove that $A, X, Y$ are collinear.