IMO Shortlist 1969 problem 46
Dodao/la:
arhiva2. travnja 2012. ![(NET 1)](/media/m/6/7/9/679039aa0ff8cabdab24f7993ab05a6b.png)
The vertices of an
![(n + 1)-](/media/m/b/f/7/bf7fac472015366b120673bd9826ce07.png)
gon are placed on the edges of a regular
![n-](/media/m/f/a/e/fae563323c2368fde7e704b858164853.png)
gon so that the perimeter of the
![n-](/media/m/f/a/e/fae563323c2368fde7e704b858164853.png)
gon is divided into equal parts. How does one choose these
![n + 1](/media/m/3/6/d/36dc98984132471cc8b030d766fd893a.png)
points in order to obtain the
![(n + 1)-](/media/m/b/f/7/bf7fac472015366b120673bd9826ce07.png)
gon with
![(a)](/media/m/a/7/f/a7fedf50ce0b917a00dd07d5233906f1.png)
maximal area;
![(b)](/media/m/9/2/7/92773ef234467079b4efc86655fdc459.png)
minimal area?
%V0
$(NET 1)$ The vertices of an $(n + 1)-$gon are placed on the edges of a regular $n-$gon so that the perimeter of the $n-$gon is divided into equal parts. How does one choose these $n + 1$ points in order to obtain the $(n + 1)-$gon with
$(a)$ maximal area;
$(b)$ minimal area?
Izvor: Međunarodna matematička olimpijada, shortlist 1969