If you consider a circle that runs through both A and B, constructed so that the circle tangent at A is equal to the initial path-segment (or the direction of the A agent):
Then you can solve for the radius r as you have a triangle where you know one angle, 90 - alpha, and one side (distance a to b) / 2.
When r is calculated, you can calculate where point c is located. With c and a and b you know how many degrees there is between the vectors c to a and c to b, divide that angle with n and you get the angle step you need to move every step to get from a to b.
Take the vector from c to a, rotate it by the angle step, the distance between that endpoint and a is the segment length you are looking for.
In the above example I am changing n, and the coordinate of b and the direction of the first segment.
I think there is some special case where c is on the other size of vector between a and b but that should be trivial to cater for.
I got pointed in the right direction by the people over at math.stackexchange (https://math.stackexchange.com/questions/4840292/given-two-points-and-a-an-angle-find-the-radius-of-the-circle-that-intersects-b)