# Stopping on a dime ...

Geometry Level 5

Let $$R$$ be the fraction of the area of a regular octagon of side length $$2$$ that lies within a distance of $$1$$ of at least one of its vertices.

If $$R$$ can be expressed as $$\dfrac{a\pi}{b}(\sqrt{c} - d)$$, where $$a,b,c,d$$ are positive integers with $$a$$ and $$b$$ being coprime and $$c$$ square-free, then find $$a + b + c + d.$$

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