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cot B + cot C >= 2/3 when medians from B,C are perpendicular

Source: 1994 Swedish Mathematical Competition p2

April 2, 2021
Geometric InequalitiesgeometryMedians

Problem Statement

In the triangle ABCABC, the medians from BB and CC are perpendicular. Show that cotB+cotC23\cot B + \cot C \ge \frac23.