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MathNet 2015-part-05 — 191 problems (EN–VI) Question 160

Math Olympiad Vault · MathNet 2015-part-05 — 191 problems (EN–VI)

Question 160

The figure shows three concentric semicircles with radii $1$, $2$, and $4$. Regions denoted by $X$ have area $x$ and regions denoted by $Y$ have area $y$. What is the ratio between areas $x$ and $y$?

Question illustration

(A) $1 : 3$ (B) $1 : 2$ (C) $2 : 3$ (D) $3 : 8$ (E) $4 : 9$