A beach ball of radius 1 foot is placed in the corner of a room so it is tangent to the floor and two of the room's walls.

geometry/ball.in.corner New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

A beach ball of radius 1 foot is placed in the corner of a room so it
is tangent to the floor and two of the room's walls.  What is the
radius of the largest ball which can be placed in the space between
the beach ball and the corner of the room?

Show solution

The ball that is in the corner has radius 1.  The center of the ball is
sqrt(3) away from the corner of the room.  The outermost edge is
sqrt(3)+1.  Innermost sqrt(3)-1.

Therefore, the ratio of radius to distance from the corner is:

            1
        ---------
        sqrt(3)+1

so, for a ball to fit inside the ball of radius of 1, it must have a
radius of:

        sqrt(3)-1
        ---------
        sqrt(3)+1

-- Richard Rognlie <rrognlie@netcom.com>