# Is that really enough info?

Geometry Level 5

Let $$R$$ and $$r$$ be the circumradius and inradius of $$\triangle ABC$$ respectively.

Given that $$R=\dfrac{7}{2 \sqrt{3}}$$ and $$r \geq \dfrac{7 \sqrt{3}}{12}$$ the maximum side length of $$\triangle ABC$$ is $$x$$.

Enter the value of $$\sqrt{4x+2}$$ as your answer.

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