Theorem relating to a system of circles

Abstract

This theorem very simply resolves a problem which can be formulated as follows as a problem of elementary geometry (see the article). Despite all the simplicity of its solution as a problem within the system of circles, it would hardly be solvable on the basis of the theorems of elementary geometry. It is clear that this theorem can be directly transferred to the system of spheres, replacing in it the words "circle" with the words "sphere". For the proof, it suffices to take the center line Q R as the axis of rotation. Thus, in its most general form, the problem of finding the centers of spherothertions of spheres is also solved, a problem which was previously solved by means of formulas.

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