Problem A. 406. (September 2006)
A. 406. 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 most three times the area of P.
(Based on the second problem of the 47th IMO, Slovenia)
Deadline expired on 16 October 2006.