Circle in a Semicircle

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Age

14 to 16

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

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?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

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Circle in a Semicircle