Inequality with angles, semiperimeter and inradius
Source: Sharygin contest. The final raund. 2008. Grade 9. First day. Problem 3
August 31, 2008
inequalitiesgeometryinradiustrigonometrygeometry unsolved
Problem Statement
(R.Pirkuliev) Prove the inequality
\frac1{\sqrt {2\sin A}} \plus{} \frac1{\sqrt {2\sin B}} \plus{} \frac1{\sqrt {2\sin C}}\leq\sqrt {\frac {p}{r}},
where and are the semiperimeter and the inradius of triangle .