Too Many Circles, Too Distracting

Geometry Level 5

Let \(I, I_a, I_b\) be the incenter, \(A-\) excenter, \(B-\) excenter respectively of a triangle \(\triangle ABC\) with side lengths \(AB= 5, BC= 7, CA= 8.\) Let \(R\) be the circumradius of \(\triangle II_aI_b.\) Find \(\sqrt{3}R.\)

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