... Geometry¹

This handout was given at the training sessions of the 6-member team, which represented USA at the International Math Olympiad this summer in Romania. Thus, do not be alarmed if you can't do most or any of the problems here, or if you do not understand some of the terminology. These certainly are not typical high school problems - rather, they are hard Olympiad-type problems. The intention of this handout is to make you think about some concepts and problems, and come to the Math Circle in September wanting to find out their interpretations and solutions.

... parabola.²

These all are conics, i.e. projectively equivalent to a circle.