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Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.

Overlapping Semicircles

Age 14 to 16 Short Challenge Level:

Two semicircles are drawn in a rectangle as shown.

What is the width of the overlap of the two semicircles?

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.