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ASU 399 All Soviet Union MO 1985 rotations and symmetry

Source:

August 5, 2019
geometrygeometric transformationrotationsymmetrycombinatorial geometry

Problem Statement

Given a straight line \ell and the point OO out of the line. Prove that it is possible to move an arbitrary point AA in the same plane to the OO point, using only rotations around OO and symmetry with respect to the \ell.