MathDB

5

Part of 2005 Turkey MO (2nd round)

Problems(1)

Geometric inequality with a,b,c,r

Source:

11/1/2010
If a,b,ca,b,c are the sides of a triangle and rr the inradius of the triangle, prove that 1a2+1b2+1c2≤14r2\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}\le \frac{1}{4r^2}
inequalitiesgeometryinradiusperimetergeometry unsolved