Problem:
Suppose that . What is the maximum possible value of
Answer Choices:
A.
B.
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D.
E.
Solution:
The graph of the equation is a square formed by the lines and . For , the equation is the equation of a circle with center and radius . Among all such circles that intersect the square, the largest one contains the points and has radius . It follows that the maximum value of is .
The problems on this page are the property of the MAA's American Mathematics Competitions