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Geometry Mathley 1.1 hexagon perimeter inequality

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June 6, 2020
geometrygeometric inequalityhexagonperimeter

Problem Statement

Let ABCDEFABCDEF be a hexagon having all interior angles equal to 120o120^o each. Let P,Q,R,S,T,VP,Q,R, S, T, V be the midpoints of the sides of the hexagon ABCDEFABCDEF. Prove the inequality p(PQRSTV)≥32p(ABCDEF)p(PQRSTV ) \ge \frac{\sqrt3}{2} p(ABCDEF), where p(.)p(.) denotes the perimeter of the polygon.
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