Problem:
Eight spheres of radius 1, one per octant, are each tangent to the coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these eight spheres?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The centers of the unit spheres are at the 8 points with coordinates , which are at a distance
from the origin. Hence the maximum distance from the origin to any point on the spheres is .
The problems on this page are the property of the MAA's American Mathematics Competitions