Difference between revisions of "2004 AIME I Problems/Problem 10"

(should have a solution soon)
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== Problem ==
 
== Problem ==
A circle of radius 1 is randomly placed in a 15-by-36 rectangle <math> ABCD </math> so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal <math> AC </math> is <math> m/n, </math> where <math> m </math> and <math> n </math> are relatively prime positive integers. Find <math> m + n. </math>
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A [[circle]] of [[radius]] 1 is randomly placed in a 15-by-36 [[rectangle]] <math> ABCD </math> so that the circle lies completely within the rectangle. Given that the p[[robability]] that the circle will not touch diagonal <math> AC </math> is <math> m/n, </math> where <math> m </math> and <math> n </math> are relatively prime positive integers. Find <math> m + n. </math>
  
 
== Solution ==
 
== Solution ==
{{solution}}
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[[Image:2004_I_AIME-10.png]]
  
 
== See also ==
 
== See also ==
* [[2004 AIME I Problems/Problem 9| Previous problem]]
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{{AIME box|year=2004|num-b=9|num-a=11}}
  
* [[2004 AIME I Problems/Problem 11| Next problem]]
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[[Category:Intermediate Geometry Problems]]
 
 
* [[2004 AIME I Problems]]
 

Revision as of 19:30, 13 October 2007

Problem

A circle of radius 1 is randomly placed in a 15-by-36 rectangle $ABCD$ so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal $AC$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$

Solution

2004 I AIME-10.png

See also

2004 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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All AIME Problems and Solutions
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