Finding the plane of intersection of two spheres in Euclidian (3D) space.

so if two spheres intersect (one with centre (1,1,2) and radius R=4 and the other with centre (1,1,4) with radius r=2) (i just made these values up i hope they work). how can you find the PLANE that is defined by the intersection of both spheres (actually it's a circle but let's call it a plane)

The normal vector of the plane is obvious, it must be the vecto C1C2 (the vector between centre 1 and centre 2)

but how do you find the known point on the sphere then?

HELP very appreciated! thanks!