The diagram shows a pattern found on a floor tile in the cathedral in Spoleto, Umbria. A circle of radius 1 surrounds four quarter circles, also of radius 1, which enclose a square. The pattern has four axes of symmetry.
What is the (exact) side length of the square? Give your expression in its simplest form.
Select one option, then click Submit.
\frac{1}{\sqrt{2}}
2 - \sqrt{2}
\frac{1}{\sqrt{3}}
\frac{1}{2}
\sqrt{2} - 1
Select an option, then submit.
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Senior Mathematical Challenge 2012 (2012)
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