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2018 AMC 10B Problems/Problem 7

Revision as of 14:29, 16 February 2018 by Cardinals2014 (talk | contribs) (Created page with "In the figure below, <math>N</math> congruent semicircles lie on the diameter of a large semicircle, with their diameters covering the diameter of the large semicircle with no...")
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In the figure below, $N$ congruent semicircles lie on the diameter of a large semicircle, with their diameters covering the diameter of the large semicircle with no overlap. Let $A$ be the combined area of the small semicircles and $B$ be the area of the region inside the large semicircle but outside the semicircles. The ratio $A:B$ is $1:18$. What is $N$?

$\textbf{(A) } 16 \qquad \textbf{(B) } 17 \qquad \textbf{(C) } 18 \qquad \textbf{(D) } 19 \qquad \textbf{(E) } 36$

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