Let $ABCD$ be the quadrilateral whose area is the largest among the quadrilaterals with given sides $a, b, c, d$, and let $PORS$ be the quadrilateral inscribed in $ABCD$ with the smallest perimeter. Find this perimeter.
Problem
Source: IV All-Ukrainian Tournament of Young Mathematicians, Qualifying p7
Tags: geometry, max, min, geometric inequality, inscribed, perimeter, Ukrainian TYM