8-9.4

Part of 2018 239 Open Mathematical Olympiad

Problems(1)

Inequality of angles

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

In a triangle, each median forms an angle with the side it is drawn to, which is less than

\alpha

. Prove that one of the angles of the triangle is greater than

180^\circ-\frac{3}{2}\alpha

. Proposed by Sergey Berlov

geometrygeometric inequalityinequalities