I'm trying to calculate coordinates of a vector that is tangential to a specific curve with known start and end coordinates, radius and length. On top of that I know the vector's length. The vector starts at the start Point of the arc. The vector has of course a starting angle, but this does not matter at the moment. I can calculate vector's coordinates when it is a chord of the arc, but this principle does not give me a result good enough. I would be grateful for any help, thanks.
Edit: I know the start and end coordinates of an arc (circular arc) with known radius as well. Therefore the equation of the curve is known. I also know the tangential vector's length and its start point.
This is a drawing I made for easier visualization of the problem:
