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Hello! I'm not a student, but need help solving a real life application (quadratic)

Hello. I have a side project I'm working on, and I am stumped. Of course, its been 25+ years since I've been in the inside of a classroom and I was always pretty shaky at math. I'll post a picture, and maybe someone can help, or direct me to the right place FOR help.

The following image represents what I'm trying to do. Its a circular graph for oilfield equipment, where there are actual pens logging various pressures. I'm not interested in that part of it, what I AM interested in is figuring out a formula that will give me the diameter of the arc to keep the areas constant with changing diameters.

Attachment 24335

On the original graph, the OD is 10", and as near as I can tell by tracing in a vector drawing program, the intersecting arc (parabola?) diameter is 22.5".

It can't be as simple as making that intersection arc 2.25 times the graph OD, can it?

I'm stumped as to where to start to figure out the intersecting arc diameter for a given OD to keep the area on the graph constant. Thanks in advance for any help!

*ETA*: I will be working with various diameters; in this graph example, its 10", I will be working with diameters ranging from 5" to roughly 25", and will need to keep the surface area constant for the different diameters. All I did was overlay circles on the arc until I got where it would trace the arc and still bisect the center of the graph, but its not exact and I don't want to eyeball it, I'd like to KNOW what the formula is for figuring it out. Again, thanks in advance.