Inequality in a cyclic quadrilateral
Source: Baltic Way 2008, Problem 17
November 23, 2008
inequalitiesgeometrygeometry unsolved
Problem Statement
Assume that , , and are the sides of a quadrilateral inscribed in a given circle. Prove that the product (ab \plus{} cd)(ac \plus{} bd)(ad \plus{} bc) acquires its maximum when the quadrilateral is a square.