Difference between revisions of "2005 AIME II Problems/Problem 12"
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== Problem == | == Problem == | ||
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Square <math> ABCD </math> has center <math> O, AB=900, E </math> and <math> F </math> are on <math> AB </math> with <math> AE<BF </math> and <math> E </math> between <math> A </math> and <math> F, m\angle EOF =45^\circ, </math> and <math> EF=400. </math> Given that <math> BF=p+q\sqrt{r}, </math> where <math> p,q, </math> and <math> r </math> are positive integers and <math> r </math> is not divisible by the square of any prime, find <math> p+q+r. </math> | Square <math> ABCD </math> has center <math> O, AB=900, E </math> and <math> F </math> are on <math> AB </math> with <math> AE<BF </math> and <math> E </math> between <math> A </math> and <math> F, m\angle EOF =45^\circ, </math> and <math> EF=400. </math> Given that <math> BF=p+q\sqrt{r}, </math> where <math> p,q, </math> and <math> r </math> are positive integers and <math> r </math> is not divisible by the square of any prime, find <math> p+q+r. </math> | ||
== Solution == | == Solution == | ||
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{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
| − | *[[2005 AIME II Problems/Problem 11| Previous problem]] | + | * [[2005 AIME II Problems/Problem 11| Previous problem]] |
| − | *[[2005 AIME II Problems/Problem 13| Next problem]] | + | * [[2005 AIME II Problems/Problem 13| Next problem]] |
* [[2005 AIME II Problems]] | * [[2005 AIME II Problems]] | ||
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| + | [[Category:Intermediate Geometry Problems]] | ||
Revision as of 22:30, 7 September 2006
Problem
Square 
has center 
and 
are on 
with 
and 
between 
and 
and 
Given that 
where 
and 
are positive integers and is not divisible by the square of any prime, find 
Solution
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