The angle between two spheres at a real point of intersection is the dihedral angle determined by the tangent planes to the spheres at that point. Two spheres intersect at the same angle at all points of their circle of intersection.. They intersect at right angles (are orthogonal) if and only if the square of the distance between their centers is equal to the sum of the squares of their radii.
tHe AnglE bETWEEn two sPHerEs At a real poINT OF InTersecTIoN Is tHe DIHedrAL angLe detERmiNeD by tHe taNgeNT plaNes to tHe SpHERes At that poinT. twO sphEreS Intersect aT The same ANGLE at all points of THeir CIrcle Of inteRSECtion.. THEy intErsecT aT riGht angLes (are ortHOgoNAl) IF and oNly if the squARe OF The distANCe bETwEen Their centers Is eqUAl to The sum oF thE squares of ThEiR RadIi.