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Circle in a Semicircle

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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.
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