1971 AHSME Problems/Problem 35
Problem
Each circle in an infinite sequence with decreasing radii is tangent externally to the one following it and to both sides of a given right angle. The ratio of the area of the first circle to the sum of areas of all other circles in the sequence, is
Solution 1
.
Solution 2 (Informed guess)
Draw a good diagram, and especially make sure that you are drawing a right angle. Then, you will realize that the big circle completely dwarfs all of the other circles. Answer choice (C), , is about , whereas the greatest of the other answer choices is about , which is unreasonably small based on our diagram. Thus, we choose answer .
See Also
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