9.6. Two spheres touch the plane of triangle $A B C$ at points $B$ and $C$ and are located on opposite sides of this plane. The sum of the radii of these spheres is 12, and the distance between their centers is $4 \sqrt{29}$. The center of a third sphere with radius 8 is located at point $A$, and it touches each of the first two spheres externally. Find the radius of the circle circumscribed around triangle $A B C$.
Answer. $4 \sqrt{5} \approx 8.94$.