MathDB
cyclic ABCD: AC > BD iff (AD-BC)(AB-CD) > 0.

Source: 2014 Sharygin Geometry Olympiad Final Round 9.1

August 3, 2018
geometrycyclic quadrilateralgeometric inequality

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. Prove that AC>BDAC > BD if and only if (AD−BC)(AB−CD)>0(AD-BC)(AB- CD) > 0.
(V. Yasinsky)
Back to ProblemsView on AoPS