# An Octagon and a Circle

Geometry Level 3

A circle is circumscribed around a regular octagon with side length 2. The area of the circle can be expressed as $$(a+b\sqrt{c})\pi$$, where $$a,b,c$$ are integers with $$c$$ square-free.

Find the sum of $$a$$, $$b$$, and $$c$$.

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