__The Hallway Problem__

The figure below represents a corner in a hallway. The diagonal line
represents a pipe that must be carried horizontally around the corner in the
hallway.

What is the longest pipe that can be carried around the corner?

To answer the question, we must find the *smallest* of all possible pipe
lengths in the diagram. Paradoxically, it is the *smallest* of these
lengths which is in fact the *longest* which would fit around the corner.

Any pipe which is longer than the smallest possible in the diagram would
intersect the walls of the hallway and would not pass horizontally through the
corner without bending. The smallest length pipe in the diagram only
intersects at the three indicated points and because it is the smallest length,
it will not intersect at any other points and will therefore just fit around the
corner.

Try changing the length of the pipe by moving the point E. Change the widths of
each hallway by moving points A, B and C.

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