~~I just noticed that in the previous image, if you draw:~~

a circle from the center of arc a, through point c.

a circle from the center of arc b, through point c.

it intersects at c, but it also intersects at the center of the arc you are looking for.

Actually, this doesn't always work, only in the example I was trying.

The center of the circle follows a parabola and you must find the value where x matches the start point of the curve.

I have no idea how to deal with parabolas though.