© 1996 Jon L. Giffen

Two spheres intersect in a circle and a third sphere doesn't intersect.
One sphere intersects two other spheres, which don't intersect each
other, forming two circles.
No mutual intersection between all 3 spheres, but in pairs; forming 3 circles.
All 3 spheres mutually intersect at 2 points.
    No position can be calculated from 3 spherical propagations except
for the last instance above.  Even then a 4th propagation is needed to
determine if the position is above or below the plane of
ABC (D or D').