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MathNet 2006 — Part 02 Question 160

Math Olympiad Vault · MathNet 2006 — Part 02

Question 160

In the figure, the three circles are concentric, and the areas of the smallest circle and the largest ring (in gray) are equal. The radius of the smallest circle is $5~\mathrm{cm}$ and the largest is $13~\mathrm{cm}$. What is the radius of the middle circle?


(A) 12

(B) 11

(C) $10 \sqrt{65}$

(D) $5 \sqrt{3}$

(E) $12 \sqrt{2}$

Question illustration