MathDB
Prove this inequality on cyclic quadrilateral

Source: 2009 Jozsef Wildt International Math Competition

April 27, 2020
geometrycyclic quadrilateralinequalities

Problem Statement

Let ABCDABCD be a quadrilateral in which A^=C^=90∘\widehat{A}=\widehat{C}=90^{\circ}. Prove that 1BD(AB+BC+CD+DA)+BD2(1AB⋅AD+1CB⋅CD)≥2(2+2)\frac{1}{BD}(AB+BC+CD+DA)+BD^2\left (\frac{1}{AB\cdot AD}+\frac{1}{CB\cdot CD}\right )\geq 2\left (2+\sqrt{2}\right )
Back to ProblemsView on AoPS