# The Star Medallion

Geometry Level 3

A pentagram is inscribed inside a circle with radius $$r$$ as shown in the picture above. The formula that puts the area of the pentagram $$S$$ in terms of the circle's radius $$r$$ can be expressed as follows:

$\large S = \dfrac{a \sqrt{10a-b\sqrt a}}c r^2 \; ,$

where $$a,b$$ and $$c$$ are positive integers with $$a$$ square-free and $$a,c$$ coprime.

Find the value of $$a+b+c$$.

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