Maths Olympiad Prep

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Geometry Difficulty 6.2 National olympiad Prove it

[28.5] Prove: For any positive integer n3n \geqslant 3, it is always possible to take nn points in the Cartesian coordinate plane such that the distance between every pair of points is an irrational number, and any three points form a non-degenerate triangle with a rational area.

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.