MathDB

Bosnia and Herzegovina TST 1999 Day 1 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 1999

September 20, 2018

inequalitiesgeometrycircumcircle

Problem Statement

Prove the inequality

\frac{a^2}{b+c-a}+\frac{b^2}{a+c-b}+\frac{c^2}{a+b-c} \geq 3\sqrt{3}R

in triangle

ABC

where

a

b

and

c

are sides of triangle and

R

radius of circumcircle of

ABC