Problem: There are two spherical balls of different sizes lying in two corners of a rectangular room, each touching two walls and the floor. If there is a point on each ball which is inches from each wall which that ball touches and 10 inches from the floor, then the sum of the diameters of the balls is
Answer Choices:
A. 20 inches
B. 30 inches
C. 40 inches
D. 60 inches
E. not determined by the given information
Solution:
In a coordinate system having corners of the room as the positive axes, a sphere with radius tangent to all three coordinate planes has an equation of the form
If the point lies on such a sphere, then
Therefore the radii of the balls are and , and the sum of the diameters is .