Second Ball above the Planes

Geometry Level 4

$\begin{eqnarray} && x + 3 y + 2 z = 5 \\ && 2x - y + z = 5 \\ && x + y - z = 5\end{eqnarray}$

In the following, it is assumed the that the $$xy$$ plane lies horizontally, and that the $$z$$ axis points upward.

Three planes are given as shown above.

A ball of radius 10 units is placed above the three planes such that it is tangent to all three of them.

Next, a second ball is to be placed above the first ball, such that it is tangent to all three planes and the first ball. What is the radius of the second ball ?

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