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
Problem
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?
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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac12$
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