There is a perfect sphere of diameter 100 cms. resting up against a perfectly straight wall and a perfectly straight floor.
What is the diameter of the largest sphere that can pass through the gap between the wall, floor and the sphere ?

My solution only works on the assumption that it doesn't matter whether we have a sphere or a circle in this problem. I'm not sure if this is correct. I'm not good at geometry. ;)

The radius of the sphere is 50cm.
The distance from the centre C of the sphere to the point where the wall and the floor meet is the diagonal of a 50*50cm square (radius of the sphere) with C as one corner, the points of tangency of the sphere with the floor and the wall (I borrowed that explanation from Charlie, I hope he doesn't mind) plus the point at which wall and floor meet as the other 3 corners.
The diagonal of a square is 1.41*side, in this case it gives 70.7107cm.

This means that the difference between the radius of the sphere and the diagonal of the square is the diameter of the second sphere which is 20.7107cm.

At least this is the solution if there were 2 circles in the problem. 8)
Edited on September 13, 2003, 4:00 pm

Posted by abc on 2003-09-13 15:51:16