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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