Solved it! Found a theorem stating that the tangent-chord angle is twice the angle of the arc. With the arc angle, I can solve for the radius by r = chord_length/(2*sin(arcangle/2)) and the rest is trigonometry.
So my problem is this: I need to figure out the center of a circle given two points. At one of the points, I know the tangent angle. So I know (x1, y1, θ1) and (x2, y2) and need to find (xc, yc). I also need to do this on a computer so I need some sort of closed-form solution.
The way I...