Question 93
Let $\triangle ABC$ be a triangle and let $J$ be the center of the excircle opposite to $A$. The reflection of $J$ in $BC$ is $K$. $E$ and $F$ are on $BJ$ and $CJ$, respectively, such that $\angle EAB = \angle CAF = 90^\circ$. Prove that $\angle FKE + \angle FJE = 180^\circ$.