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The diagram shows a square of area $x$ square units inscribed inside a semicircle and a larger square of area $y$ square units inscribed inside a circle.
What is the ratio $x : y$ ?

 

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.