Difference between revisions of "2005 AIME II Problems/Problem 8"
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== See Also == | == See Also == | ||
| + | *[[2005 AIME II Problems/Problem 7| Previous problem]] | ||
| + | *[[2005 AIME II Problems/Problem 9| Next problem]] | ||
*[[2005 AIME II Problems]] | *[[2005 AIME II Problems]] | ||
[[Category:Intermediate Geometry Problems]] | [[Category:Intermediate Geometry Problems]] | ||
Revision as of 20:58, 7 September 2006
Problem
Circles 
and 
are externally tangent, and they are both internally tangent to circle 
The radii of and are 4 and 10, respectively, and the centers of the three circles are all collinear. A chord of 
is also a common external tangent of and 
Given that the length of the chord is 
where 
and 
are positive integers, 
and are relatively prime, and 
is not divisible by the square of any prime, find 
Solution
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