Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 1.8 Junior Find the answer

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 $N$ ?

Pick one

Solution

Use the answer choices and calculate them. The one that works is $\bold{\boxed{\text{(D)19}}}$ .
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Note: This solution is time-consuming and is not recommended.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.