2006 AMC 12A Problems/Problem 16

Revision as of 19:07, 5 November 2006 by Xantos C. Guin (talk | contribs) (added category)

Problem


An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.


Circles with centers $A$ and $B$ have radii $3$ and $8$, respectively. A common internal tangent intersects the circles at $C$ and $D$, respectively. Lines $AB$ and $CD$ intersect at $E$, and $AE=5$. What is $CD$?

$\mathrm{(A) \ } 13\qquad \mathrm{(B) \ } \frac{44}{3}\qquad \mathrm{(C) \ } \sqrt{221}\qquad \mathrm{(D) \ } \sqrt{255}$$\mathrm{(E) \ }  \frac{55}{3}$

Solution

See also