2020 AMC 12B 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 \qquad\textbf{(B)}\ 98 \qquad\textbf{(C)}\ 44\sqrt5 \qquad\textbf{(D)}\ 70\sqrt2 \qquad\textbf{(E)}\ 100

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.