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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