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7 points inside or on a regular hexagon, with (ABC)<1/6 hexagon area

Source: Mexican Mathematical Olympiad 1992 OMM P3

July 29, 2018
geometryarea of a trianglehexagon

Problem Statement

Given 77 points inside or on a regular hexagon, show that three of them form a triangle with area 1/6\le 1/6 the area of the hexagon.