2313. 
A rectangular box contains a sphere of radius and eight smaller spheres of radius . The smaller spheres are each tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres. What is ?
This problem is copyrighted by the American Mathematics Competitions.

Instructions for entering answers:
For questions or comments, please email markan@eudelic.com.
Try our new, free contest math practice test. All new, neverseenbefore problems.
I offer online AMC/AIME classes periodically. Join the mailing list to be informed next time they're offered.
Private coaching is also available.