Question 25
Let $ABC$ be a triangle with $AB \lt AC$. Let $M$ be the midpoint of $BC$. Line $l$ is drawn through $M$ so that it is perpendicular to $AM$, and intersects line $AB$ at point $X$ and line $AC$ at point $Y$. Prove that $\angle BAC = 90^{\circ}$ if and only if quadrilateral $XBYC$ is cyclic.