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Difference between revisions of "2019 AMC 10B Problems/Problem 16"

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In <math>\triangle ABC</math> with a right angle at <math>C,</math> point <math>D</math> lies in the interior of <math>\overline{AB}</math> and point <math>E</math> lies in the interior of <math>\overline{BC}</math> so that <math>AC=CD,</math> <math>DE=EB,</math> and the ratio <math>AC:DE=4:3.</math> What is the ratio <math>AD:DB?</math>
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<math>\textbf{(A) }2:3\qquad\textbf{(B) }2:\sqrt{5}\qquad\textbf{(C) }1:1\qquad\textbf{(D) }3:\sqrt{5}\qquad\textbf{(E) }3:2</math>

Revision as of 13:51, 14 February 2019

In $\triangle ABC$ with a right angle at $C,$ point $D$ lies in the interior of $\overline{AB}$ and point $E$ lies in the interior of $\overline{BC}$ so that $AC=CD,$ $DE=EB,$ and the ratio $AC:DE=4:3.$ What is the ratio $AD:DB?$

$\textbf{(A) }2:3\qquad\textbf{(B) }2:\sqrt{5}\qquad\textbf{(C) }1:1\qquad\textbf{(D) }3:\sqrt{5}\qquad\textbf{(E) }3:2$

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