Tangent spheres

A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it?

Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and tangent to each other.

Correct result:

r =  0.2679 m

Solution:

$$\begin{gathered} R=1\text{ m } \\ u=\sqrt{3}\cdot R=\sqrt{3}\cdot 1=\sqrt{3}\text{ m}\doteq 1.7321\text{ m } \\ x=u-R=1.7321-1\doteq 0.7321\text{ m } \\ x=r+\sqrt{3}r \\ r=x\mathrm{/}(1+\sqrt{3})=0.7321\mathrm{/}(1+\sqrt{3})=0.2679\text{ m} \end{gathered}$$

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