Difference between revisions of "2001 AIME I Problems/Problem 5"

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== Problem ==
 
== Problem ==
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An equilateral triangle is inscribed in the ellipse whose equation is <math>x^2+4y^2=4</math>. One vertex of the triangle is <math>(0,1)</math>, one altitude is contained in the y-axis, and the length of each side is <math>\sqrt{\frac mn}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.
  
 
== Solution ==
 
== Solution ==
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{{solution}}
  
 
== See also ==
 
== See also ==
* [[2001 AIME I Problems/Problem 4 | Previous Problem]]
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{{AIME box|year=2001|n=I|num-b=4|num-a=6}}
 
 
* [[2001 AIME I Problems/Problem 6 | Next Problem]]
 
 
 
* [[2001 AIME I Problems]]
 

Revision as of 23:21, 19 November 2007

Problem

An equilateral triangle is inscribed in the ellipse whose equation is $x^2+4y^2=4$. One vertex of the triangle is $(0,1)$, one altitude is contained in the y-axis, and the length of each side is $\sqrt{\frac mn}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution

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See also

2001 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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All AIME Problems and Solutions
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