3 circles mutually tangent to each other

I was trying to draw 3 circles mutually tangent to each other in context of understanding the Descarte's theorem which give rise to Appolinius Gasket. First Descarte's theorem. It says that if there are 3 kissing circles than there exists two circles which kiss all these 3 circles and the curvature has a beautiful formula (b1+b2+b3+b4)^2 = 2(b1^2+b2^2+b3^2+b4^2) where b4 gives two values and hence two circles. One can solve for b4 and after some yuckky algebra it can be shown that its b4 =(b1+b2+b3) +-2(b1.b2+b2.b3+b3.b1)^(1/2). The cool thing about Apollinian Gasket is that the whole gasket can be inverted into itself. Sort of infinite reflection when two parallel mirrors are placed. and then the two roots of quadratic can be expressed more easily as d1 = 2(b1+b2+b3)-d2
It has interesting history behind it because people didn't find the last form for almost 200 yrs. Here is the attached file which shows how one can draw 3 kissing circles. Drawing two kissing circles is straightward. To draw the 3 draw an arbitrary circle centred on any one circle and then the difference b/w this and arbitrary circle should be added to the other circle. the intersection of these two will give you pair of pts which will be equidistant from the original 2 circles and now one can draw a 3rd circle kissing the other two.