Find if 3d point is inside 3d Circle

Hi all

I have been trying to find the correct and comprehensive algorithm to find if any giving point in space is inside a known circle(s) (i.e X Y Z radius angle azimuth).

I tried doing it by just finding the distance between the center of the circle and the point but this however can not accurately measure the points that are just outside the circle and belong to other circle. This is because I am testing if that particular point belong to many different circles in the space.

This is what I am using at the momment (x - x_centre)^2 + (y - y_centre)^2 + (z - z_centre)^2 <= r^2

Any ideas ?

Thanks