My Technic math puzzle of the day

[N. W. Perry]

I made an animation to help me visualize it, see attached zip.

Determining if the stop has gone to far is relatively easy.

So I'm thinking the solution to the main question is doable by writing the self contained formulas of the two values I compare in that test.

And then apply some substitution black magic on them to find the common angle value.

edit: minor correction (for the perfectionists)

Code:

applyColor(info.refStopper, p:getX(), {min=0, max=i:getX()-10, orgCol=7})

should be

Code:

applyColor(info.refStopper, p:getX(), {min=0, max=i:getX()-9, orgCol=7})

Now if I can just figure out how to extract those formulas. (You're going to have me learning lua whether I like it or not!)

EDIT:
Hmm, now that I watch the animation, I notice that, in fact, there are not multiple possible solutions where the distance to D is equal to 19—at least, none that are also within the constraints of the shock length. There is only one point where the liftarm touches both the control arm and the stopper piece; everywhere else, it touches only the control arm.