First, construct three tangent circles (blue circles), then construct the triangle joining their centers. Then construct three Malfatti Circles for this triangle (green circles). Go on.
What I'm asking is this - it appears that the radii of the green circles are closer together, than the radii of the blue cirlces. I.e., if the radius of a blue circle is $R_k$ and the green circle $r_k$, then we have:
$$\frac{\max{R_k}}{\min{R_k}} \geq \frac{\max{r_k}}{\min{r_k}},~~~k=1,2,3$$
Where equality is supposed to be only for three equal cirlces.
Is this true for any initial three cirlces? Does it mean, that this iteration will have three equal cirlces as a limit?
I know that there are formulas for the radii of the Malfatti Circles, but they are very complicated and I would appreciate it if someone gives me a quick answer. If not, I will have to do a lengthy calculation.