MathDB

Geometric inequality with a,b,c,r

Source:

November 1, 2010

inequalitiesgeometryinradiusperimetergeometry unsolved

Problem Statement

a,b,c

are the sides of a triangle and

r

the inradius of the triangle, prove that

\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\le \frac{1}{4r^2}