x^(2)+y^(2) = r^(2)

=> y^(2) = r^(2)-x^(2)

=> y = √(r^(2)-x^(2))

=> y-y0 = √(r^(2)-x^(2))-y0

y-y0 is the distance from the circle to a chord, where y0 is the distance from the centre of the chord to the circle and x is the distance along the chord relative to the centre of the chord.

If you're trying to construct an arc which is a relatively small portion of the circle, that's probably the most useful formula.