An Outstanding Inequality in an arbitrary hexagon, ZIMO - 09
Source: International Zhautykov Olympiad 2009, day 1, problem 3.
January 17, 2009
inequalitiesgeometrytrigonometrytrig identitiesLaw of Cosinesgeometry proposed
Problem Statement
For a convex hexagon with an area , prove that:
AC\cdot(BD\plus{}BF\minus{}DF)\plus{}CE\cdot(BD\plus{}DF\minus{}BF)\plus{}AE\cdot(BF\plus{}DF\minus{}BD)\geq 2\sqrt{3}S