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 October 16, 2006.
11 students sent a solution. 5 points: Gyenizse Gergő, Gyürke Csaba, Kornis Kristóf, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Szűcs 003 Gábor, Tomon István. 4 points: Korándi Dániel. 3 points: 1 student.