2005 AIME II Problems/Problem 8
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 
