tetrahedron ABCD : circumsphere and insphere

a = (ax, ay, az)  ...  d = (dx, dy, dz)  are the coordinates of the vertices,
Nabc  is a cross product, thus a vector orthogonal to the plane (ABC).
The coordinates of the centers SC of the circumsphere and SI of the insphere,
   just as their respective radii R and r, express themselves with determinants and norms.


formulae