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Chisinau MO p28 1949-56 VIII-IX 2\sqrt{(p-b)(p-c)} <= a

Source:

March 15, 2021
geometric inequalitygeometryinequalities

Problem Statement

Prove the inequality 2(p−b)(p−c)≤a2\sqrt{(p-b)(p-c)}\le a, where a,b,ca, b, c are the lengths of the sides, and pp is the semiperimeter of some triangle..
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