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The diagram shows a right-angled isosceles triangle $XYZ$ which circumscribes a square $PQRS$. What is the ratio of the area of square $PQRS$ to the area of the triangle $XYZ$?

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.
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