Parallel lines plus more.

[Oddgamer]

Sorry for posting again. The problem I have has changed a lot, and I'm not sure I described it well the first time. So, I'm back with some pictures and to make sure I've got it all worked out.
Okay, I have a series of concentric rings, each ring defined by pairs of circles about some mid-point o, both of known (but variable) radii. The below pictures show a single ring.

In the above, I know the angle aob (though it can vary) from the first picture, I then need points c, d, e, and f from the next picture (notice they are parallel to the ob line, they are not radii of those circles, and the distance between c and the line b is known but variable, call it w). Then for each of the next four pictures I need the point g given I know gh (the radius, this can vary, too), and some way to work out the angle hgi and igk (the start and stop points where the circle with center g touches the cd or ef line and continues to touch the nearby larger circle for the ring). All of this should allow me to come up the ring separated along the line b by width w with the corners rounded off.

 

[Oddgamer]

Another way to look at the problem would be to define each arc instead.

In the pictures, we'd have AoB and AoC (note! 0 is not necessarily the origin... I realized that later. In my case it's going to be somewhere else). In the second picture we'd need AoD (with the radius oD being known) and DoF, then similar for the next one with AoG and GoH, then for the last picture points J and K (there'd be two more at the other end, along with their own angles) then angles MJN and NJP for the first circle and QKR and RKT for the second circle. The reason for the position is that, starting from straight up and moving clockwise, I'd need to know where to start drawing and how much of an angle to draw.
This entire process is slightly less secure since it relies on the circles meeting up exactly (no misses) to avoid gaps where rounding errors occur. And, of course, the angles AoB and AoC aren't fixed.