The question on how to create parametric tangential arcs in families (ex: structural section profiles, extrusion sketches, etc.) seems to come up quite often. And it can be done in Revit: it’s just not as straight-forward.
An AUGI thread resurrected this discussion last month and in my opinion, it was approaching the question from the wrong end. Sure, you can do complicated trigonometric formulas to solve this (I know, I am the Count (Formula) after all!), but it is best to avoid them if at all possible. Intuition says that if you keep things simple and parameterize through simple labels (no calculated parameters), everything should run faster, leaner and more efficient.
So you be the judge. Should you go with this (source: BIM and Beam):
You be the judge! The key is to use the "Tangent End Arc" type and then constrain along both sides to set where the center of the arc is, (no need to parameterize the arc’s radius). More details can be found in the AUGI post.
EDIT: And even more detail can be found here on Steve’s blog!