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Math Prize 2017 Problem 17

Source:

September 27, 2017
Math Prize for Girls

Problem Statement

Circle ω1\omega_1 with radius 3 is inscribed in a strip SS having border lines aa and bb. Circle ω2\omega_2 within SS with radius 2 is tangent externally to circle ω1\omega_1 and is also tangent to line aa. Circle ω3\omega_3 within SS is tangent externally to both circles ω1\omega_1 and ω2\omega_2, and is also tangent to line bb. Compute the radius of circle ω3\omega_3.
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