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3

Part of 1993 Mexico National Olympiad

Problems(1)

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

Source: Mexican Mathematical Olympiad 1993 OMM P3

7/29/2018
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.
combinatorial geometrygeometrypentagonarea of a triangle