CEMC Pascal, 2000

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

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

(A) $2.5\pi$ (B) $5\pi$ (C) $\pi$ (D) $2.5\pi+5$ (E) $2.5\pi-2.5$

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