# A strange side length

**Geometry**Level 4

A regular polygon inscribed in a unit circle has a side length of \[\large \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}} .\]

Find the number of sides of the polygon.

A regular polygon inscribed in a unit circle has a side length of \[\large \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}} .\]

Find the number of sides of the polygon.

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