Hey. I have a question on Descartes Circle Theorem:

is a circle with radius r.

and are two equal circles that touch at a point T, and with a common tangent L. The circle touches both and externally and also shares the common tangent L. There exists a chain of circles for such that touches and externally. Find in terms of r.

I shall try and supply a picture.

Using inversion, I've worked out that . However, I would like to derive this using Descartes Circle Theorem. Any ideas?