I want to move one object (dot) in a circular path. How should I change the X and Y coordinates to accomplish this?
You can make it by using simple math.
Origin is the center of your circle. Size is the radius of that circle. Thats it.
There's another trick, where you use the sin(x+a) and cos(x+a) formulas, and that allows you to compute sin(a) and cos(a) -- a being the angle by which you want to move from your current position -- only once and do simply multiplication and additions at each step.
sin(x+a) = sin(x)*cos(a) + cos(x)*sin(a), iirc.
Of course, that assumes constant angular velocity.