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Product of the radii of three circles doesn't exceed A

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September 23, 2010
trigonometrygeometric inequalityTriangleIMO Shortlist

Problem Statement

Prove that the product of the radii of three circles exscribed to a given triangle does not exceed A=338A=\frac{3\sqrt 3}{8} times the product of the side lengths of the triangle. When does equality hold?
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