Can you use angles? if so, the arc formula or the law of cosines ought to do it. If not, I don't know what to tell you.
The above picture is a visualization of my problem (Programming, yay!).
What is labeled on the picture is what I know.
How would I be able to pick a point on the circle (the blue part) and solve for the coordinates of the point.
It has been awhile T.T
Well the equation for a circle is In your problem, none of these values x, y, or r are "known." So it's difficult to give you any kind of an answer without having some known values; particularly the location of the center of the large circle, as well as its radius. Without these, the problem makes little sense, so far as I can tell.