2000 Pascal Problem 21

ABCD is a rectangle with AD=10. If the shaded area is 100, then the shortest distance between the semicircles is

\textbf{(A)}\ 2.5\pi\quad \textbf{(B)}\ 5\pi\quad \textbf{(C)}\ \pi\quad \textbf{(D)}\ 2.5\pi+5\quad \textbf{(E)}\ 2.5\pi-2.5

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.