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min |(cot A + cot B)(cot B + cot C)(cot C + cot A)| in ABC

Source: Indonesia INAMO Shortlist 2010 G7

August 27, 2021
geometrygeometric inequalitytrigonometryinequalities

Problem Statement

In triangle ABCABC, find the smallest possible value of ∣(cot⁡A+cot⁡B)(cot⁡B+cot⁡C)(cot⁡C+cot⁡A)∣|(\cot A + \cot B)(\cot B +\cot C)(\cot C + \cot A)|
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