Sangaku Geometry Theorem: Three circles and a tangent line

In the figure below, three circles of radiii: a, b, c are mutually tangent to each other and a line. Prove that: .
 

References: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton University Press, 2008).

See also:
Geometry problem 1154
Geometric art version 1

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