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995 points inside the pentagon of area 1993, at least 3 points (ABC)<=1

Source: Mexican Mathematical Olympiad 1993 OMM P3

July 29, 2018
combinatorial geometrygeometrypentagonarea of a triangle

Problem Statement

Given a pentagon of area 19931993 and 995995 points inside the pentagon, let SS be the set containing the vertices of the pentagon and the 995995 points. Show that we can find three points of SS which form a triangle of area ≤1\le 1.
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