The blue circle has radius 2 and the green circle has radius 1 AB is a common tangent and all 3 circles touch each other. Find the radius of the smallest circle. The answer is btw 6 - 4√2 how ever I'm only getting as to far as (6-2√2)/7
Please solve with working

The blue circle has radius 2 and the green circle has radius 1 AB is a common tangent and all 3 circles touch each other Find the radius of the smallest circle class=