To achieve this I think I have to use the arch from 3 points. All those 3 points are the exact tangent points on the other circle and the two reference lines.

Not absolutely nessecary, but it would preferrable.
There are 9 other families in the system and, if possible, I’d like to stay with the same method for all of them. This way I can reuse common sub-families easier.

Here is a screenshot of the whole system:
(I am talking about the corner element)