I made a rough depiction in paint so assume the red lines divide the big circle exactly by half and both circle's circumferences collide in a single point at the top of the vertical red line.
If you find a link to the geometrical property/ratio/whatever used to solved this please post it
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Something tells me that you'll use the difference in the measured values along with arc length properties to figure it out. That said, I don't feel like pursuing that right now.