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

Abstract

Imaginary circles play a very important role in solving geometric and crystallographic problems. Imaginary spheres also play a significant role. However, in solving certain problems related to some of the simplest sets of imaginary circles and spheres, as problems of an elementary geometric nature, difficulties arise that are easily resolved precisely due to the simple properties of these sets. The article discusses possible ways to solve these problems.

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