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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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