Problem:
A circle with center is tangent to the positive - and -axes and externally tangent to the circle centered at with radius 1 . What is the sum of all possible radii of the circle with center
Answer Choices:
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Solution:
Let be the radius of a circle with center , and . Then, and . Applying the Pythagorean Theorem to gives
Also, , so , which simplifies to . Thus , both of which are positive, and the sum of all possible values of is .
The problems on this page are the property of the MAA's American Mathematics Competitions