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PORS inscribed in ABCD with max area given sides, where PQRS has min perimeter

Source: IV All-Ukrainian Tournament of Young Mathematicians, Qualifying p7

May 19, 2021
geometrymaxmingeometric inequalityinscribedperimeterUkrainian TYM

Problem Statement

Let ABCDABCD be the quadrilateral whose area is the largest among the quadrilaterals with given sides a,b,c,da, b, c, d, and let PORSPORS be the quadrilateral inscribed in ABCDABCD with the smallest perimeter. Find this perimeter.
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