IMO Shortlist 2002 problem G5
Dodao/la:
arhiva2. travnja 2012. For any set
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
of five points in the plane, no three of which are collinear, let
![M(S)](/media/m/e/3/b/e3bc11c912b7a5e7facc6ae20f162044.png)
and
![m(S)](/media/m/e/7/c/e7c8c27e006f905840bc7f87034e3fb9.png)
denote the greatest and smallest areas, respectively, of triangles determined by three points from
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
. What is the minimum possible value of
![M(S)/m(S)](/media/m/4/0/2/4029401929c587b3fdfd1218c6aa91c6.png)
?
%V0
For any set $S$ of five points in the plane, no three of which are collinear, let $M(S)$ and $m(S)$ denote the greatest and smallest areas, respectively, of triangles determined by three points from $S$. What is the minimum possible value of $M(S)/m(S)$ ?
Izvor: Međunarodna matematička olimpijada, shortlist 2002