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Maximal angles between medians and sides

Source: IZhO 2024, P6

January 11, 2024
geometry

Problem Statement

Let GG be the centroid of triangle ABCABC. Find the biggest α\alpha such that there exists a triangle for which there are at least three angles among ∠GAB,∠GAC,∠GBA,∠GBC,∠GCA,∠GCB\angle GAB, \angle GAC, \angle GBA, \angle GBC, \angle GCA, \angle GCB which are ≥α\geq \alpha.
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