Question 98
Let $ABC$ be a triangle with $\angle ABC = 90^{\circ}$. Points $D$ and $E$ on $AC$ and $BC$ respectively satisfy $BD \perp AC$ and $DE \perp BC$. The circumcircle of $\triangle CDE$ intersects $AE$ at two points, $E$ and $F$. Prove that $BF \perp AE$.