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

$\textbf{(A) }(4+3\sqrt{2}):4\qquad \textbf{(B) }9\sqrt{2}:2\qquad \textbf{(C) }(16+12\sqrt{2}):1\qquad \\ \textbf{(D) }(2+2\sqrt{2}):1\qquad \textbf{(E) }(3+2\sqrt{2}):1$

Solution

$\boxed{\textbf{(C) }(16+12\sqrt2):1}$ .

1971 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 34	Followed by Last Problem
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1971 AHSME Problems/Problem 35

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