Mock AIME 1 2006-2007/Problem 10
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Problem
In 
, 
, 
, and 
have lengths 
, 
, and 
, respectively. Let the incircle, circle 
, of touch , , and at 
, 
, and 
, respectively. Construct three circles, 
, 
, and 
, externally tangent to the other two and circles , , and are internally tangent to the circle at , , and , respectively. Let circles , , , and have radii 
, 
, 
, and 
, respectively. If 
where 
and 
are positive integers, find 
.
Solution
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