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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Too Many Circles, Too Distracting

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.