AMC 12 2020b Problem 12

Let $\overline{AB}$ be a diameter in a circle of radius $5\sqrt2.$ Let $\overline{CD}$ be a chord in the circle that intersects $\overline{AB}$ at a point $E$ such that $BE=2\sqrt5$ and $\angle AEC = 45^{\circ}.$ What is $CE^2+DE^2?$

\textbf{(A)}\ 96 \textbf{(B)}\ 98 \textbf{(C)}\ 44\sqrt5 \textbf{(D)}\ 70\sqrt2 \textbf{(E)}\ 100