Arc and a Straight Line Tangent to Spline Curve

I have a problem which I was hopping to get some help on. I’m trying to use grasshopper to draw an arc of given radius tangent both to a straight line of given length which passes through a fixed point and to a parabola/spline curve. I’ve attached a picture which will hopefully help clarify what I am trying to do. The two parameters that are not constrained are the angle of the straight line (alpha) and the angle of the arc (beta). I would appreciate it if someone could help me draw this shape using grasshopper for any given curve, straight length, and radius. I’ve included a grasshopper file with the point and curve internalized as a starting point. I appreciate any help and suggestions.

Tangent Straight (6.8 KB)