MathDB

58

Part of 1977 IMO Longlists

Problems(1)

Nice geometric inequality of IMO LongList 1977

Source:

1/11/2011
Prove that for every triangle the following inequality holds: ab+bc+ca4S≥cot⁡π6.\frac{ab+bc+ca}{4S} \geq \cot \frac{\pi}{6}. where a,b,ca, b, c are lengths of the sides and SS is the area of the triangle.
inequalitiesgeometrytrigonometryarea of a triangleHeron's formulageometry proposed