Difference between revisions of "2004 AIME I Problems/Problem 10"
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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 | + | 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 == | ||
− | + | [[Image:2004_I_AIME-10.png]] | |
== See also == | == See also == | ||
− | + | {{AIME box|year=2004|num-b=9|num-a=11}} | |
− | + | [[Category:Intermediate Geometry Problems]] | |
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Revision as of 19:30, 13 October 2007
Problem
A circle of radius 1 is randomly placed in a 15-by-36 rectangle so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal is where and are relatively prime positive integers. Find
Solution
See also
2004 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |