/sci/ - Science & Math

>>9187676
I had a similar problem a while back.
I wanted to construct these circles with only compass and straightedge,
which I managed to do by using inversion
(https://en.wikipedia.org/wiki/Inversive_geometry))

the idea behind this is, that inversion maps some circles onto lines which are easier to handle, while preserving geometric properties like intersections.
That way you change the original problem of finding a circle that touches 3 circles exactly once into a much easier problem, which is to find a circle that lies between 2 parallel lines and touches another circle exactly once.
From there on you can do some nasty calculations to find out, what the radius of those inscribed circles is.
Here's my solution which I have verified with geogebra
[eqn]
r_n = \frac{1}{2r_0\left (\left ( \frac{\sqrt{3}}{3r_0^2-1}+n \right )^2 -\frac{1}{4} \right)}
[/eqn]