Difference between revisions of "2005 AIME II Problems/Problem 14"
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== Problem == | == Problem == | ||
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In triangle <math> ABC, AB=13, BC=15, </math> and <math>\displaystyle CA = 14. </math> Point <math> D </math> is on <math> \overline{BC} </math> with <math> CD=6. </math> Point <math> E </math> is on <math> \overline{BC} </math> such that <math> \angle BAE\cong \angle CAD. </math> Given that <math> BE=\frac pq </math> where <math> p </math> and <math> q </math> are relatively prime positive integers, find <math> q. </math> | In triangle <math> ABC, AB=13, BC=15, </math> and <math>\displaystyle CA = 14. </math> Point <math> D </math> is on <math> \overline{BC} </math> with <math> CD=6. </math> Point <math> E </math> is on <math> \overline{BC} </math> such that <math> \angle BAE\cong \angle CAD. </math> Given that <math> BE=\frac pq </math> where <math> p </math> and <math> q </math> are relatively prime positive integers, find <math> q. </math> | ||
== Solution == | == Solution == | ||
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{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
| − | *[[2005 AIME II Problems/Problem 13| Previous problem]] | + | * [[2005 AIME II Problems/Problem 13| Previous problem]] |
| − | *[[2005 AIME II Problems/Problem 15| Next problem]] | + | * [[2005 AIME II Problems/Problem 15| Next problem]] |
* [[2005 AIME II Problems]] | * [[2005 AIME II Problems]] | ||
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| + | [[Category:Intermediate Geometry Problems]] | ||
Revision as of 21:34, 7 September 2006
Problem
In triangle 
and 
Point 
is on 
with 
Point 
is on such that 
Given that 
where 
and 
are relatively prime positive integers, find 
Solution
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