Semicircle Distance
Age 14 to 16
ShortChallenge Level 
The diagram shows a rectangle and two semicircles.
The height of the rectangle 10 cm, and the area of the shaded region is 125 cm$^2$.
What is the shortest distance between the two semicircles?
Give your answer in terms of $\pi$.
This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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