Difference between revisions of "2002 AIME I Problems/Problem 13"
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== Problem == | == Problem == | ||
| − | In triangle <math>ABC</math> the medians <math>\overline{AD}</math> and <math>\overline{CE}</math> have lengths 18 and 27, respectively, and <math>AB=24</math>. Extend <math>\overline{CE}</math> to intersect the circumcircle of <math>ABC</math> at <math>F</math>. The area of triangle <math>AFB</math> is <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers and <math>n</math> is not divisible by the square of any prime. Find m+n. | + | In triangle <math>ABC</math> the medians <math>\overline{AD}</math> and <math>\overline{CE}</math> have lengths 18 and 27, respectively, and <math>AB=24</math>. Extend <math>\overline{CE}</math> to intersect the circumcircle of <math>ABC</math> at <math>F</math>. The area of triangle <math>AFB</math> is <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers and <math>n</math> is not divisible by the square of any prime. Find <math>m+n</math>. |
== Solution == | == Solution == | ||
Revision as of 17:14, 25 September 2007
Problem
In triangle 
the medians 
and 
have lengths 18 and 27, respectively, and 
. Extend to intersect the circumcircle of at 
. The area of triangle 
is 
, where 
and 
are positive integers and is not divisible by the square of any prime. Find 
.
Solution
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