Hey macleodjb.

How much calculus do you know?

The reason is that you will know the tangent for the start and ends of the circle since you know the angles and you you have a formula regarding what the derivatives are for a given circle with an equation x^2 + y^2 = r^2 and the dy/dx will correspond to the gradient as a function of the angle.

So you have two gradients so you will essentially get a relation to where the (x,y) points are for the circle part (you get two solutions and discard one for each tangent) and this will give you the relative points for that circle which gives the (x,y) points at the two positions.