Too Many Circles, Too Distracting

Geometry Level 5

Let I,Ia,IbI, I_a, I_b be the incenter, AA- excenter, BB- excenter respectively of a triangle ABC\triangle ABC with side lengths AB=5,BC=7,CA=8.AB= 5, BC= 7, CA= 8. Let RR be the circumradius of IIaIb.\triangle II_aI_b. Find 3R.\sqrt{3}R.

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