MathDB

37

Part of 1985 IMO Longlists

Problems(1)

Inequality in a triangle

Source:

9/13/2010
Prove that a triangle with angles α,β,γ\alpha, \beta, \gamma, circumradius RR, and area AA satisfies tan⁡α2+tan⁡β2+tan⁡γ2≤9R24A.\tan \frac{ \alpha}{2}+\tan \frac{ \beta}{2}+\tan \frac{ \gamma}{2} \leq \frac{9R^2}{4A}.
[hide="Remark."]Remark. Can we determine all of equality cases ?
inequalitiesgeometrycircumcircletrigonometryarea of a triangleHeron's formulainequalities unsolved