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Calculating the rotation of two points on a circle

Hello Everyone!

I have been pondering over a problem for a while now and can not seem to find the answer.

Lets say I have a circle, and two points on the circle. Let assume "c" is the center of the circle, "a" is one point and "b" is another point. Also not that AC = BC and AC is perpendicular to BC. With that being said, lets say at one moment in time I know the exact location of "a", "b", and "c", then at a later moment I also measure the points "a", "b", and "c". "c" has remained the same, but "a" and "b" have along the circumference of the circle to new locations. (I have attached some pictures below as a visual aid).

My question is how would I measure the rotation of points "a", and "b" around the circle. I would preferably measure this in radians or angle if possible. I done similar math to this but am unfamiliar with the algebraic way of solving such a problem. Does anyone have any advice for suggestions, they would be greatly appreciate.

Attachment 18473

Thanks,

Taylor S. Amarel

Learning is living.