if a line bisect perimeter then this line bisects the area
Source: Sharygin contest 2008. The correspondence round. Problem 20
September 3, 2008
geometryperimetergeometry proposed
Problem Statement
(A.Zaslavsky, 10--11) a) Some polygon has the following property:
if a line passes through two points which bisect its perimeter then this line bisects the area of the polygon. Is it true that the polygon is central symmetric?
b) Is it true that any figure with the property from part a) is central symmetric?