There are 4 solid spheres arranged so that each one is touching all of the others. The 3 bottom spheres touch the flat floor at points A, B and C. The top sphere has a radius of 12 centimeters. If it were replaced by a sphere with radius 25 cm, then its center would be 14, 15 and 16 cm further from from points A, B and C, respectively.

What is the radius of each sphere?