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Angle AIO is less than 90 degrees iff 2a =<b+c

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November 7, 2010
geometryincentertrigonometrygeometry unsolved

Problem Statement

Let II be the incentre and OO the circumcentre of a non-equilateral triangle ABCABC. Prove that ∠AIO≤90∘\angle AIO \le 90^{\circ} if and only if 2BC≤AB+AC2BC\le AB+AC.
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