ARMO 2019 9.1
Source: All-Russian Math Olympiad 2019
July 11, 2019
ARMOcombinatoricscombinatorial geometry
Problem Statement
There are 5 points on plane. Prove that you can chose some of them and shift them such that distances between shifted points won't change and as a result there will be symetric by some line set of 5 points.