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 19:58, 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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