20

Part of 2008 Sharygin Geometry Olympiad

Problems(1)

if a line bisect perimeter then this line bisects the area

Source: Sharygin contest 2008. The correspondence round. Problem 20

(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?

geometryperimetergeometry proposed