Two spheres intersect in a circle (which will be imaginary unless they are close enough together) which lies in a plane perpendicular to the line joining their centers. But we need to know the radius of the circle and how far along the line joining the two centers it lies. These quantities are not difficult to obtain by using a modest amount of trigonometry, but there is an interesting formulation of the problem via projective geometry [4,2] which includes various limiting cases. Among them are point spheres and spheres of infinite radius, which are planes.