Biggest k
Source: Iranian National Olympiad (3rd Round) 2006
September 19, 2006
functiongeometryinradiuscircumcircleinequalitiesincenterinequalities unsolved
Problem Statement
Find the biggest real number such that for each right-angled triangle with sides , , , we have
a^{3}\plus{}b^{3}\plus{}c^{3}\geq k\left(a\plus{}b\plus{}c\right)^{3}.