# 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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