The second drawing [Tangential Arc Problem 4] illustrates the last (and probably the most difficult) case I deal with. In this case, point Z is a known location and an arc must be constructed from a tangent point on arc XY to point Z tangent to line AC. The drawing represents the CAD solution drawn using snap tangents to show point C2 and R2. I have no idea how to even begin on a mathematical solution for this. I understand if this is too complex to get into on these forums and I don't want to be a bother, so if you are unable to assist with this last case, do you have someplace you could recommend I can go to online to review constructions such as this? Thanks again. You've been a great help.