Question 79
Chords $\overline{AB}$ and $\overline{CD}$ of circle $\omega$ intersect at $E$ such that $AE=8$, $BE=2$, $CD=10$, and $\angle AEC=90^{\circ}$. Let $R$ be a rectangle inside $\omega$ with sides parallel to $\overline{AB}$ and $\overline{CD}$, such that no point in the interior of $R$ lies on $\overline{AB}$, $\overline{CD}$, or the boundary of $\omega$. What is the maximum possible area of $R$?
