Difference between revisions of "2001 AIME I Problems/Problem 5"
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== Problem == | == Problem == | ||
+ | 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 == | ||
+ | {{solution}} | ||
== See also == | == See also == | ||
− | + | {{AIME box|year=2001|n=I|num-b=4|num-a=6}} | |
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Revision as of 23:21, 19 November 2007
Problem
An equilateral triangle is inscribed in the ellipse whose equation is . One vertex of the triangle is , one altitude is contained in the y-axis, and the length of each side is , where and are relatively prime positive integers. Find .
Solution
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See also
2001 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |