TITLE: Finding radius of the central radius?
QUESTION [5 upvotes]: Is there any easy way to get the radius of the central  radious?

REPLY [3 votes]: This is a more general approach : We consider several layers of circles with $n$ circles per layer. The layers are numbered $ 1 , 2, 3, ... k, ...$. The small inner circle is not included ( there are $n$ circles in the layer number 1 ).
The next figure shows the notations and how the recurrence formula is derived, leading to the relationship between the radius of the circles of the k-ieme layer and the radius of the circles of the first layer.
 
Comming back to the case considered in the question raised by "Complex Guy", there are 2 layers. The radius of the circles in layer 2 is given. Applying the above formula leads to the formula for the radius of the small inner circle.