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A sphere with a radius of 8 sits in the corner, touching the floor and two walls. A smaller sphere sits between the sphere, touching the floor, the walls, and the larger sphere. What is the radius of the smaller sphere?

I tried to create the smallest cube possible that would fit a sphere with radius 8, and use the long diagonal to determine the diameter of the smaller sphere, but i'm not sure that's correct.

Any and all help is appreciated!

user978757
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    Related: https://math.stackexchange.com/questions/2644700/whats-new-in-higher-dimensions/2644740#2644740 – Ethan Bolker Oct 27 '21 at 22:32
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    Hint: Try drawing the 2D cross-section of these spheres with the floor below and wall on one side – Mufasa Oct 27 '21 at 22:33
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    Choose a coordinate system where the walls/floor intersect at origin and the volume they enclose is the first octant. The centers of the small/large ball are $(r,r,r)$ and $(8,8,8)$. What is the distance between these two centers? – achille hui Oct 28 '21 at 00:08

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