The center of the circle on the sphere will not project as the center of the circle on the plane. The formula for the radius of the projected circle differs only in the middle sign, which is negative instead of positive. If we want to construct a stereonet in the standard orientation with the great circles like meridians of longitude, then the circle that represents longitude w will have its pole at longitude w plus or minus 90. The minus sign in the distance formula simply means that the center of the circle lies on the opposite side of the sphere from the meridian. The formulas suggest the simple construction at left.
Linear dimensions are in red, angles in purple.
Point C is the center of the great circle. It's useful to have some formula that relates distance AO and angle w. For the small circles of the stereonet, a always equals 90 because the circles are centered on the pole. Thus, a circle of latitude l has radius 90-l. The simple construction at left can be used to plot a small circle of latitude l.