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Semicircle in a Semicircle

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2
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The diagram shows two semicircular arcs, PQRS and QOR . The diameters, PS and QR , of the two semicircles are parallel; PS is of length 4 and is a tangent to semicircular arc QOR .

What is the area of the shaded region?

Semicircular arcs

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



This problem is taken from the UKMT Mathematical Challenges.