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Difference between revisions of "2023 AMC 12B Problems/Problem 3"

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==Problem==
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A 3-4-5 right triangle is inscribed circle <math>A</math>, and a 5-12-13 right triangle is inscribed in circle <math>B</math>. What is the ratio of the area of circle <math>A</math> to circle <math>B</math>?
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<math>\textbf{(A) }\frac{9}{25}\qquad\textbf{(B) }\frac{1}{9}\qquad\textbf{(C) }2\frac{1}{5}\qquad\textbf{(D) }\frac{25}{169}\qquad\textbf{(E) }3\frac{4}{25}</math>

Revision as of 13:18, 15 November 2023

Problem

A 3-4-5 right triangle is inscribed circle $A$, and a 5-12-13 right triangle is inscribed in circle $B$. What is the ratio of the area of circle $A$ to circle $B$?

$\textbf{(A) }\frac{9}{25}\qquad\textbf{(B) }\frac{1}{9}\qquad\textbf{(C) }2\frac{1}{5}\qquad\textbf{(D) }\frac{25}{169}\qquad\textbf{(E) }3\frac{4}{25}$

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