IMO 2006 Shortlist G10
To each side a of a convex polygon we assign the maximum area of a triangle contained in the polygon and having a as one...
Category: Geometry
Problem
To each side a of a convex polygon we assign the maximum area of a triangle contained in the polygon and having a as one of its sides. Show that the sum of the areas assigned to all sides of the polygon is not less than twice the area of the polygon. (Serbia)