There's something I am missing comparing Descartes' theorem for three isometric circles here and this wiki post on circle packing of 3 circles here.

From my calculation:

$$ r_{ext} = \frac{r_{int}}{{(3\pm2\sqrt3)}}, \tag{1} $$

where *r _{ext}* is the external radius and

*r*the internal radius. In the second article it seems:

_{int}$$ r_{ext} = r_{int}(1+2\frac{\sqrt3}{3}). \tag{2} $$

(Probably is crappy mathematics of my own.)

For the sake of completness. The generic formula I derived from Descartes' theorem is (for different radii):

$$ r_{ext} = \frac{r_{1}r_{2}r_{3}}{(r_{1}r_{2}+r_{2}r_{3}+r_{1}r_{3} \pm 2{\sqrt{r_{1}r_{2}r_{3}(r_{1}+r_{2}+r_{3})}{}})}. \tag{3} $$

what am I missing?