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Round and Round

Age 14 to 16
Challenge Level Yellow starYellow star
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Prove that the shaded area of the semicircle is equal to the area of the inner circle.

Circle inside semicircle

What percentage of the sector OAB is taken up with the inner circle?

Circle inside quarter circle

What happens if angle AOB is less than 90 ° or between 90 and 180 degrees?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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