# Circles in a circle

Geometry Level 4

Given that there are three identical circles with radius $$r$$, each touches each other on their respective circumferences and they are all inscribed in a circle with radius $$R$$. If the ratio of $$r$$ to $$R$$ can be expressed as

$\large \dfrac1{\frac a{\sqrt b} + c}$

for positive integers $$a,b$$ and $$c$$ with $$b$$ square-free, find the value of $$a+b+c$$.

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