Difference between revisions of "2006 AMC 12A Problems/Problem 16"

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[[Category:Introductory Geometry Problems]]

Revision as of 19:07, 5 November 2006

Problem


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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