Difference between revisions of "2005 AIME I Problems/Problem 15"

Revision as of 21:51, 16 December 2006

Triangle $ABC$ has $BC=20.$ The incircle of the triangle evenly trisects the median $AD.$ If the area of the triangle is $m \sqrt{n}$ where $m$ and $n$ are integers and $n$ is not divisible by the square of a prime, find $m+n.$

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 == Problem ==
-Triangle <math> ABC </math> has <math> BC=20. </math> The incircle of the triangle evenly trisects the median <math> AD. </math> If the area of the triangle is <math> m \sqrt{n} </math> where <math> m </math> and <math> n </math> are integers and <math> n </math> is not divisible by the square of a prime, find <math> m+n. </math>
+[[Triangle]] <math> ABC </math> has <math> BC=20. </math> The [[incircle]] of the triangle evenly [[trisect]]s the [[median of a triangle | median]] <math> AD. </math> If the [[area]] of the triangle is <math> m \sqrt{n} </math> where <math> m </math> and <math> n </math> are [[integer]]s and <math> n </math> is not [[divisor | divisible]] by the [[square]] of a [[prime]], find <math> m+n. </math>
 == Solution ==
+{{solution}}
 == See also ==
+* [[2005 AIME I Problems/Problem 14 | Previous problem]]
 * [[2005 AIME I Problems]]
+[[Category:Intermediate Geometry Problems]]