MathDB

sin A/2 sin B /2 sin C/ 2 < 1/ 4.

Source: Vietnamese MO (VMO) 1970

August 23, 2018

trigonometryTrigonometric inequalitygeometryinequalities

Problem Statement

Prove that for an arbitrary triangle

ABC

sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2} < \frac{1}{4}