Mock AIME 4 2006-2007 Problems/Problem 15
Problem
Triangle 
has sides 
, 
, and 
of length 43, 13, and 48, respectively. Let 
be the circle circumscribed around 
and let 
be the intersection of and the perpendicular bisector of 
that is not on the same side of as 
. The length of 
can be expressed as 
, where 
and 
are positive integers and is not divisible by the square of any prime. Find the greatest integer less than or equal to 
.
Solution
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