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Rose has a spherical plum of radius $2$ and a spherical watermelon of radius $8$.  She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible.  When she has done this, she places a golf ball inside the glass sphere that is tangent to the plum and watermelon.  What is the largest possible radius of the golf ball?

 
 Sep 3, 2023

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