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0123 geo inequality 1st edition Round 2 p3

Source:

May 9, 2021
geometric inequality1st editiongeometryinequalities

Problem Statement

Prove that in any acute triangle with sides a,b,ca, b, c circumscribed in a circle of radius RR the following inequality holds: 24<Rp2aR+bc<12\frac{\sqrt2}{4} <\frac{Rp}{2aR + bc} <\frac{1}{2} where pp represents the semi-perimeter of the triangle.