Theorem relating to the circle system

Abstract

This theorem very simply solves the problem, which can be formulated as follows as a problem of elementary geometry (see article). Despite the simplicity of solving it as a problem in a system of circles, it is hardly solvable on the basis of theorems of elementary geometry. It is clear that this theorem can be directly transferred to the system of spheres by replacing the words “circle” with the words “sphere”. To prove it, it is enough to take the central Q R as the axis of rotation. Thus, in the most general form, the problem of finding the centers of spherotions of sphers, which was previously solved through formulas, is resolved.