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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