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# Semicircle Distance

##### Age 14 to 16 Short Challenge 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.