The radii of the four tangent circles are related to each other according to Descartes circle theorem:
If we define the curvature of the nth circle as: 

The plus sign means externally tangent circle like circles r_{1} , r_{2} , r_{3} and r_{4} and the minus sign is for internally tangent circle like circle r_{5} in the drawing in the top.
Then the Descartes circle theorem is: 
( k_{1} + k_{2} + k_{3} + k_{4} ) ^{2} = 2 ( k_{1}^{2} + k_{2}^{2} + k_{3}^{2} + k_{4}^{2} ) 
