Problem:
Abdul and Chiang are standing feet apart in a field. Bharat is standing in the same field as far from Abdul as possible so that the angle formed by his lines of sight to Abdul and Chiang measures . What is the square of the distance (in feet) between Abdul and Bharat?
Answer Choices:
A.
B.
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E.
Solution:
In the diagram below-an overhead view-points , and represent the locations of Abdul, Bharat, and Chiang, respectively. Let be the circle containing , and , and let be center of . Because , it follows that .
Because is as far as possible from , it follows that must be at the other end of the diameter of containing , as shown.
It remains to calculate . Because is a right triangle and , it follows that . Then
The problems on this page are the property of the MAA's American Mathematics Competitions