SHARYGIN 2008 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?
Dataset text AI-MO AoPS. Quoted with source.
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