HELP how do I lock the endpoints of an arc to reference planes?

I have intersecting reference planes to which I need to lock the endpoints of an arc, so that when I put a radius parameter on the arc, the endpoints stay in one place and the middle of the arc moves up or down. I can't seem to get it to work, the arc keeps moving concentrically about the original centerpoint whenever I change the radius. Anybody know how to make it work?

Well I was able to make it work by placing invisible model lines at the points where the arc endpoints and center would be, locking those model lines to reference planes, but then to make the reference plane for the centerpoint move and the endpoints stay in place, I had to enter an equation of the pythagorean theorem in reverse to get the vertical distance from the endpoints to the centerpoint (square root of the radius squared minus half the endpoint distance squared).

Surely there has to be an easier way to do that? It took me over an hour just to make a parametric brick arch family that can be placed over windows or doors or openings, and the width and radius be adjusted to match the radius and width of the door or window.

I attached the family if anybody wants to take a look at it, or use it for their own projects. :mrgreen:

Note: you will have to add model lines after the arch is placed for the brick coursing... I haven't figured out how to do that yet in the family... I'm sure it will involve more formulas.