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Circle in a Semicircle

Age 14 to 16 Short Challenge Level:

The diagram shows a semi-circle containing a circle which touches the circumference of the semicircle and goes through its centre. What fraction of the semicircle is shaded?

Semi Circle containing a circle

 

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.