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Putting 1987 points (IMO SL 1987-P13)

Source:

August 19, 2010
geometryIMOIMO 1987IMO Shortlistcoordinate geometryarea

Problem Statement

Is it possible to put 19871987 points in the Euclidean plane such that the distance between each pair of points is irrational and each three points determine a non-degenerate triangle with rational area? (IMO Problem 5)
Proposed by Germany, DR