Question 52
At some moment, three different points were marked in the plane. After that, at each minute three marked points are chosen (denote them by $A$, $B$, $C$), and a point $D$ symmetrical to $A$ with respect to the perpendicular bisector to $BC$ is marked.
A day later, it appeared that there exist three collinear marked points. Prove that three initial points are also collinear. (V. Shmarov)
A day later, it appeared that there exist three collinear marked points. Prove that three initial points are also collinear. (V. Shmarov)