Question 824160
Note that the two square root equations are equations for two sphere's with centers at (B, C, D) and (E, F, G) and the square roots represent the radius of their respective spheres.  That is,
let t' = sqrt( (X-B)^2 + (Y-C)^2 + (Z-D)^2 )  and
t'' = sqrt( (X-E)^2 + (Y-F)^2 + (Z-G)^2 ) 
sphere one
X = B + t' * cos(theta) cos(phi)
Y = C + t' * cos(theta) sin(phi)
Z = D + t' * sin(theta) 
and 0 <= theta < 2 pi, and -pi/2 <= phi <= pi/2
sphere two
X = E + t'' * cos(theta) cos(phi)
Y = F + t'' * cos(theta) sin(phi)
Z = G + t'' * sin(theta) 
and 0 <= theta < 2 pi, and -pi/2 <= phi <= pi/2
therefore we have
A = 0 if t' = t''
A > 0 if t' > t''
A < 0 if t' < t''