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
638^{2} + 720^{2} = 962^{2}
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.
