2

Part of 1999 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 1999 Day 1 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 1999

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

ABC

a

b

c

are sides of triangle and

R

radius of circumcircle of

ABC

inequalitiesgeometrycircumcircle