Okay, I think I've made a little progress...I just realized it's a regular 40-gon overlying the circle.
(Except it differs from the above in that it's resting on a side, not on a point. Just a slight rotation.)
This at least gives the question some more structure...what I'm trying to do, I guess, is figure out how much each point differs from the other in horizontal and vertical coordinates. If I can get that, I can do an x, y, z to x2, y2, z2 distance calculation and get the sides of the triangle.
Any idea what the rate of change is? Like, how much does it go up for each subsequent side of the 40-gon?