From the given values AD=BD=CD This is useful since that means the circumcenter of ABC will coincide with the orthogonal projection of D onto ABC; and the center of the sphere will lay on the line containing D and its projection.
So then ABC has sides 7.2, 9.6, and 12. By the Pythagorean theorem this is a right triangle, so the diameter of the circumcircle is 12, and the circumcenter is the midpoint of diameter BC.
Then BCD is an isosceles triangle with sides 12, 15.6 and 15.6 and its circumcenter is the center of the sphere. So then I grabbed the formula for the circumradius of a triangle to get R=12*15.6*15.6/sqrt[43.2*12*12*19.2] = 8.45.
Solution
