MathDB
1/a + b +1/(a+c)+1/(b+c) \leq r/16Rs+ s/16Rr + 11/8s

Source: Balkan MO Shortlist 2015 A2

August 5, 2019
geometryinradiuscircumradiussemiperimeterinequalitiesgeometric inequality

Problem Statement

Let a,b,ca,b,c be sidelengths of a triangle and r,R,sr,R,s be the inradius, the circumradius and the semiperimeter respectively of the same triangle. Prove that: 1a+b+1a+c+1b+c≤r16Rs+s16Rr+118s\frac{1}{a + b} + \frac{1}{a + c} + \frac{1}{b + c} \leq \frac{r}{16Rs}+\frac{s}{16Rr} + \frac{11}{8s}
(Albania)
Back to ProblemsView on AoPS