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'Weekly Problem 19 - 2006' printed from http://nrich.maths.org/

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Three semicircles enclosing an area

The diagram shows three semicircles, each of radius one. What is the size of the total area shaded?
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.

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