Question: I wonder if you can help me develop an equation on polar form for the position of the center of gravity for the circular spandrel

I wonder if you can help me develop an equation on polar form for the position of the center of gravity for the circular spandrel marked with yellow lines (see figure attached)? The position of the center of gravity should be described in relation to the centre of the circle. The centre of gravity will then lay outside of the circle as can be seen from the figure, and be dependent on the radius of the circle and the angles theta_1 and theta_2.
I wonder if you can help me develop an equation

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