I am trying to find a construction to do the following. I want to have two lines tangent to the three circles roughly as shown. However, I need a 60 degree angle between the lines.

The black circles cannot move. The red circle can move tangent to the line to the right of it.

How then would one position the red circle along the line so that the tangents would be at 60 degrees?

I do not see any solution to that - the black circles need to move to hold the 60 degrees, or the angle needs to increase to leave the black circles in place.

Ah, Ok - so you are allowing rotation of the lines… still the solution looks likely to be iterative, to me - I am not sure that there is an exact construction for this.

the orange curves represent the 0.035 offset with the inscribed angle / circle for 60 degree
the violet surface shows all possible tangents
the cyan surface is to construct the rails for the green surface
the green surface should be a (non-existing) sweep2 with road like top option - and this is where this approach gets un-precise…
the green, final circle is 3x tangent, but has a radius of 0.0348889 inches (instead of 0.035)…

Yeah, @Tom_P - that’s the way I understood it as well. Easily done in SWX, but not sure if there’s a way to construct it without dependencies/parametry.
-Jakob