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scent of a classic area inequality (2013 HOMC Junior Q6)

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July 18, 2019
geometrygeometric inequalityareasarea of a triangle

Problem Statement

Let ABCABC be a triangle with area 11 (cm2^2). Points D,ED,E and FF lie on the sides AB,BCAB, BC and CA, respectively. Prove that min{min\{area of △ADF,\vartriangle ADF, area of △BED,\vartriangle BED, area of △CEF}≤14\vartriangle CEF\} \le \frac14 (cm2^2).
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