IMO Shortlist 2006 problem G10
Dodao/la:
arhiva2. travnja 2012. Assign to each side
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
of a convex polygon
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
the maximum area of a triangle that has
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
as a side and is contained in
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
. Show that the sum of the areas assigned to the sides of
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
is at least twice the area of
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
.
%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 $P$.
Izvor: Međunarodna matematička olimpijada, shortlist 2006