3 symmetric points after finite no of steps lie outside a circle
Source: II All-Ukrainian Tournament of Young Mathematicians, Qualifying p16
May 20, 2021
geometrysymmetrySymmetricUkrainian TYM
Problem Statement
Inside the circle are given three points that do not belong to one line. In one step it is allowed to replace one of the points with a symmetric one wrt the line containing the other two points. Is it always possible for a finite number of these steps to ensure that all three points are outside the circle?