Sectors in a Square

Geometry Level 3

Two touching sectors are drawn centred on opposite corners of a square of sidelength 4.

If the total perimeter of the sectors can be expressed in the form \(\sqrt{c}(a\pi+b)\) where \(a\), \(b\) and \(c\) are integers and \(c\) is a prime, find \(a+b+c\).

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