SOLUTION: https://files.fm/u/3shp85xkx

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Question 1202026: https://files.fm/u/3shp85xkx
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Consider the right angle bisector, which goes from the center 
of the large circle to the tangent point of two circles.


Write equation for the length of this angle bisector


    r + r%2Asqrt%282%29 = 14.


Simplify it and express "r"


    r*(1 + sqrt%282%29) = 14,


    r = 14%2F%281%2Bsqrt%282%29%29 = 5.799 cm  (rounded).

Solved.