Help Needed co-ordinate boundarys

I am writing a program which creates a set of coordinates that when plotted will reveal a syastro crescent moon character. If you imagine plotting a crescent moon as two circles with different radius, where the overlap will create the shape. The problem I am having is how to just plot where they overlap ( ie the crescent moon part) and no the rest of the circles. How can I impose a boundary to stop the program creating coordinates I dont want. My first attempt is an if else loop but suggestions are welcome.

Thanks
What I would do is have a separate image surface to work with; make the background all one color, draw the smaller circle (the moon), and then draw the bigger circle as the background color. This effectively leaves only the part left over.
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