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Solution to Puzzle 127.  CIRCULAR AMPHITHEATER

A king wanted to build a circular amphitheater on a site which had been the ruins of an old fortress.  On this site, only three pillar had remained.  The king wanted to preserve those three pillars.  He asked his royal architects to design a circular amphitheater so that these pillars would be along the circumference of the amphitheater.  The distances of these pillars from each other were 720 feet, 962 feet, and 638 feet respectively.  What would be the radius of the amphitheater to be built? 

Solution:

It can be noted that 

6382 + 7202 = 9622

This means that the three pillars are vertices of a right triangle.  A circle passing thru these three vertices would circumscribe the right triangle, with its diameter equal to the hypotenuse of the right triangle.  The diameter of the circular amphitheater would therefore be 962 feet, and its radius would be 481 feet.

 

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The Last Recreations:  Hydras, Eggs, and Other Mathematical Mystifications

Author:  Martin Gardner

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