I could easily be missing the entire point here,… but it seems to me that the dashed line you’ve drawn in is highlighting the intersection of the two larger construction circles.
…and so the two tangent markings you’ve made come from only one of the construction circles.
… with it’s second companion tangent only matching up with one of the little outside tensioning circles (for lack of better words).
In this sense there is no common arc for either of the two mid size circles to share a tangent with… BUT you may know this already… so I’m not sure if I’m just trying to clarify my own confusion here… or maybe my comments can add to something a little better than that. (??)