A geometry problem by Rishabh Tiwari

Geometry Level 4

Find the length of the side of smallest equilateral triangle in which three disks of radii 2, 3, and 4 can be placed without overlap?

If the answer is of the form $$b\sqrt{c}$$, where $$b$$, and $$c$$ are positive integers and $$c$$ is square-free. Find $$b + c$$.

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