IMO Shortlist 2006 problem G10
Assign to each side
of a convex polygon
the maximum area of a triangle that has
as a side and is contained in
. Show that the sum of the areas assigned to the sides of
is at least twice the area of
.
%V0
Assign to each side $b$ of a convex polygon $P$ the maximum area of a triangle that has $b$ as a side and is contained in $P$. Show that the sum of the areas assigned to the sides of $P$ is at least twice the area of $P$.
Source: Međunarodna matematička olimpijada, shortlist 2006
Školjka 
