Three natural homotheties of the nine-point circle (Q2871660)

The paper under review is concerned with the configuration consisting of a triangle, the reflections of its vertices about the respective sidelines, the pedal circles of these reflections, and the nine-point circle of the triangle. It turns out that the three pedal circles mentioned above are images of the nine-point circle under certain homotheties and that their centers form the anticevian triangle of the nine-point center. Many other properties of the configuration are established.