## How to calculate the radii of closed Steiner chains?

I would like to know how to calculate the series of n radii in a closed Steiner chain where C1 is the outer circle & C2 is the inner circle such that the centres of C1 & C2 are on the foci of an ellipse upon which the centres of the Steiner chain circles lie.
I've read a lot of pages showing how to calculate the ellipse but I haven't come across anything that shows how to calculate the series of radii in the corresponding closed Steiner chain.
I understand that there will be an infinite number of Steiner chains all of the same n but what is the relationship between the n radii?

PS I didnt really know where to put this question as it didnt seem to fit in the pre-uni section so I put it here.