4.2. Three spheres touch each other pairwise; a plane touches these spheres at points $A, B$, and $C$. Find the radii of the spheres if the sides of triangle $ABC$ are equal to $a, b$, and $c$.
4.2. Let $x, y$ and $z$ be the radii of the spheres. According to problem 4.1, $a=2 \sqrt{x y}, b=2 \sqrt{y z}$ and $c=2 \sqrt{x z}$. Therefore, $a c / b=2 x$, hence $x=a c / 2 b$. Similarly, $y=a b / 2 c$ and $z=b c / 2 a$.