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2008 AMC 12A Problems/Problem 20

Revision as of 22:05, 18 February 2008 by Garyzx (talk | contribs) (New page: ==Problem== Triangle <math>ABC</math> has <math>AC=3</math>, <math>BC=4</math>, and <math>AB=5</math>. Point <math>D</math> is on <math>\overline{AB}</math>, and <math>\overline{CD}</math>...)
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Problem

Triangle $ABC$ has $AC=3$, $BC=4$, and $AB=5$. Point $D$ is on $\overline{AB}$, and $\overline{CD}$ bisects the right angle. The inscribed circles of $\triangle ADC$ and $\triangle BCD$ have radii $r_a$ and $r_b$, respectively. What is $r_a/r_b$?

$\textbf{(A)}\ \frac{1}{28}\left(10-\sqrt{2}\right) \qquad \textbf{(B)}\ \frac{3}{56}\left(10-\sqrt{2}\right) \qquad \textbf{(C)}\ \frac{1}{14}\left(10-\sqrt{2}\right) \qquad \textbf{(D)}\ \frac{5}{56}\left(10-\sqrt{2}\right) \\ \textbf{(E)}\ \frac{3}{28}\left(10-\sqrt{2}\right)$

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