55th International Mathematical Olympiad

摘要

Inversion is a conformal map; that is, it preserves angles locally. Inversion also maps circles to other circles, where lines are circles of infinite radius. More specifically, circles through H map to lines not through H, and vice versa. Also, lines through H map to themselves, and circles not through H map to circles not through H. After inverting at H, our diagram becomes FIGURE 3, where the notation P0 is used to indicate the image of P, and H is left in the diagram.