Some elementary geometric theorems and problems related to collections of imaginary circles and spheres

Abstract

Imaginary circles play a very important role in solving geometric and crystallographic problems. Imaginary spheres also play a huge role. But when solving some problems related to some simple sets of imaginary circles and spheres, as problems of an elementary geometric nature, difficulties arise that are easily eliminated precisely thanks to the simple properties of these sets. The article discusses possible ways to solve these problems.