Mathematical and Physical Journal
for High Schools
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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)

(5 pont)

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.

Problems in Mathematics of KöMaL, September 2006