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 ?

(√5000)-50 is the answer.
Draw a line from the centre of the large circle to the base of the wall. This is the hypotenuse of a triangle formed by dropping a perpendicular from the centre to the floor. That is %0cm and so is the floor part. Use Pythagoras and deduct the radius leaving the diameter of the new small circle. QED.

Posted by Denis Cronin on 2003-09-21 18:49:33