Question 79
Let $ABC$ be a triangle with $\angle BAC = 60^\circ$. The points $D$ and $E$ lie on the sides $AC$ and $AB$ respectively. The lines $BD$ and $CE$ meet the circumcircle of $ABC$ again at the points $X$ and $Y$ respectively. Let $S$ be the intersection point of $BD$ and $CE$. Prove that the lines $BY$ and $CX$ are parallel if and only if $AESD$ is a cyclic quadrilateral.