One of the properties of tangent circles

Abstract

We have two equal mutually tangent circles O1 O2. We have a straight line AB, tangent to both, and a new circle C, tangent to both data. We assert that the point of intersection of these two tangents, i.e. points D and E, as well as the point of tangency of two given circles, i.e. point F, are equally distant from point G, i.e. from one of the meeting points of the circle C and straight CF. Proof of Prof. E.S. Fedorov.