Finding circle center from two points and arc angle

I'm trying to find the equation for a circle given two points in Cartesian coordinates and the starting angle, arc length, and two points along the circle. I need to find the equation because I need to translate a sprite along the curved path from one point to another.

The situation ends up looking like this:

----c C
A = point 1
B = point 2
C = center of the circle
the arc travels from a to b
c = arc angle

Now, I can clearly determine the length of all sides as well as the angles. thats not problem. I can use that to make a system of equations and solve them together. This works, but the problem is that I need to be able to do this programmatically, and attempting to solve systems of equations in C++ is proving to be pretty difficult. I was hoping there was a more straight forward/easy way to find the center point when two points are know, and all the angles/lengths are known to the 3rd point (center).

Thanks in advance for any help

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Oct 30, 2011
Cartesion Coordinate equation
by: Rakiya

The general formula to a cartesian coordinate is:

(X-a)² + (Y-b)²=r²

a and b are the x and y coordinates of the center of the circle.

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