So given that the 4 vertices of a triangular pyramid pass through a sphere S and given the centre of the sphere and the volume of the pyramid,

how can you verify (prove) that the centre lies OUTSIDE that pyramid?

the sphere's centre is (6,3,2) and the radius is 14. the vertices are A(12,0,0) B(0,6,0) C(0,0,4) and the origin (0,0,0).

help much appreciated!! thanks!