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'Weekly Problem 42 - 2006' printed from http://nrich.maths.org/

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$AB$ is a diameter of a circle of radius 1 cm. Two circular arcs of equal radius are drawn with centres $A$ and $B$. These arcs meet on the circle, as shown. What is the shaded area? Circle
 
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This problem is taken from the UKMT Mathematical Challenges.

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