Initially, there are three different points on the plane. Every minute, three points are chosen, for example A, B and C, and a new point D is generated which is symmetric to A with respect to the perpendicular bisector of line segment BC. 24 hours later, it turns out that among all the points that were generated, there exist three collinear points. Prove that the three initial points were also collinear. (Author: V. Shmarov) geometrycircumcircleperpendicular bisectorgeometry proposed