Inequality for a triangle with C >= 60°
Source: China TST 1990, problem 5
June 27, 2005
inequalitiestrigonometrygeometry solvedgeometry
Problem Statement
Given a triangle with angle . Prove that:
\left(a \plus{} b\right) \cdot \left(\frac {1}{a} \plus{} \frac {1}{b} \plus{} \frac {1}{c} \right) \geq 4 \plus{} \frac {1}{\sin\left(\frac {C}{2}\right)}.