Difference between revisions of "2000 AIME II Problems/Problem 11"
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== Problem == | == Problem == | ||
| − | + | The coordinates of the vertices of isosceles trapezoid <math>ABCD</math> are all integers, with <math>A=(20,100)</math> and <math>D=(21,107)</math>. The trapezoid has no horizontal or vertical sides, and <math>\overline{AB}</math> and <math>\overline{CD}</math> are the only parallel sides. The sum of the absolute values of all possible slopes for <math>\overline{AB}</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}} | {{solution}} | ||
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== See also == | == See also == | ||
{{AIME box|year=2000|n=II|num-b=10|num-a=12}} | {{AIME box|year=2000|n=II|num-b=10|num-a=12}} | ||
Revision as of 18:36, 11 November 2007
Problem
The coordinates of the vertices of isosceles trapezoid 
are all integers, with 
and 
. The trapezoid has no horizontal or vertical sides, and 
and 
are the only parallel sides. The sum of the absolute values of all possible slopes for is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
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See also
| 2000 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
