Problem

1991 AHSME Problem 19

[asy] draw((0,0)--(0,3)--(4,0)--cycle,dot); draw((4,0)--(7,0)--(7,10)--cycle,dot); draw((0,3)--(7,10),dot); MP("C",(0,0),SW);MP("A",(0,3),NW);MP("B",(4,0),S);MP("E",(7,0),SE);MP("D",(7,10),NE); [/asy]

Triangle $ABC$ has a right angle at $C, AC=3$ and $BC=4$ . Triangle $ABD$ has a right angle at $A$ and $AD=12$ . Points $C$ and $D$ are on opposite sides of $\overline{AB}$ . The line through $D$ parallel to $\overline{AC}$ meets $\overline{CB}$ extended at $E$ . If $\frac{DE}{DB}=\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers, then $m+n$ is

$\textbf{(A) } 25\qquad \textbf{(B) } 128\qquad \textbf{(C) } 153\qquad \textbf{(D) } 243\qquad \textbf{(E) } 256$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

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Category: AHSME
Points: 2
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