Finding random intersecting line

Okay, so I have kind of a problem.

I have two points (A, B), and I want to find two other Points (C,D) which create a line that intersects the line AB. It doesn’t matter where it intersects, aslong as it doesn’t touch point A or B (Like a Random generator to create an obstacle). The Points A and B are Vector3(x,y,0), the line is drawn by a LineRenderer. C should be anywhere on the blue circle and D anywhere on the red circle.
The Line CD is drawn by a LineRenderer too.

i would do this:

1- add collider to the AB line, so can be detected by next line.

2 -create a point C at rnadom place, and with a collider bigger than the point be sure it does not touch the line (this means C is not touching A / B).

3 -Then create point D and do the same to detect A B or C

4 -generate the CD line with a collider and detect if is detecting AB line. if not, need to restart from point 3 of this list.

Byee!

Ok, at first thought, I’d say find the angles of the points on the boundary (simple trigonometry) then find the points, so that one point is strictly inside the a-b range and the other is strictly outside outside. The point on the boundary depending on the angle will be r*(cos(x), sin(x)), where r is the circle radius.