chord of a polygon questions, area bisector, area>=1/3 of area of polygon
Source: VI All-Ukrainian Tournament of Young Mathematicians, Qualifying p9
May 25, 2021
geometrychordpolygonareaUkrainian TYM
Problem Statement
Consider an arbitrary (optional convex) polygon. It's chord is a segment whose ends lie on the boundary of the polygon, and itself belongs entirely to the polygon. Will there always be a chord of a polygon that divides it into two equal parts? Is it true that any polygon can be divided by some chord into parts, the area of each of which is not less than the area of the polygon?