Parametrisation of an angle for an arc

The positions of A' and B' are controled with sliders.

I have managed to parametrize the point B'° in a way, that:

when t = 0 ==> B' = B'°

when t = 1 ==> B'° moves on a circular arc until the y-coodrinate of B'° be the same as the y-coordinate of A' (A' is the center of the arc)

Now I'm trying to make an arc between the two points in Grasshopper ...

Is there some arc component, that can get this done with minimum of energy and time?! I have been on this since today morning!!