I believe here's the key:
1. Create a circle with B as center, and the radius should get through A2 and C... let's call this circle HELPER
2. Rotate this circle with A2 as pivot point, in particular ways, so that IF we draw 3 point circle from A1, A2, and B, then the circle WILL intersect HELPER along with the V Axis and C.

BUT, this will take several steps before we get the wanted result after zooming execisevely to the intersection point mentioned in number 2.

Just a crazey idea.