Eyelids

Can you work out the shaded area surrounded by these arcs?
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Problem



$AB$ 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?
Image
Eyelids


 

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