The vertices of an gon are placed on the edges of a regular gon so that the perimeter of the gon is divided into equal parts. How does one choose these points in order to obtain the gon with maximal area; minimal area?
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$(NET 1)$ 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
Školjka 
The vertices of an 
gon are placed on the edges of a regular 
gon so that the perimeter of the 
points in order to obtain the 
maximal area;
minimal area?