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Inequality of angles

Source: 239 Open MO 2018, Junior League, Problem 4

April 4, 2023
geometrygeometric inequalityinequalities

Problem Statement

In a triangle, each median forms an angle with the side it is drawn to, which is less than α\alpha. Prove that one of the angles of the triangle is greater than 180∘−32α180^\circ-\frac{3}{2}\alpha. Proposed by Sergey Berlov
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