Difference between revisions of "1985 AIME Problems/Problem 9"
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== Problem == | == Problem == | ||
| − | + | In a [[circle]], [[parallel]] [[chord]]s of [[length]]s 2, 3, and 4 determine [[central angle]]s of <math>\alpha</math>, <math>\beta</math>, and <math>\alpha + \beta</math> [[radian]]s, respectively, where <math>\alpha + \beta < \pi</math>. If <math>\cos \alpha</math>, which is a [[positive]] [[rational number]], is expressed as a [[fraction]] in lowest terms, what is the sum of its [[numerator]] and [[denominator]]? | |
== Solution == | == Solution == | ||
| − | + | {{solution}} | |
== See also == | == See also == | ||
| + | * [[1985 AIME Problems/Problem 8 | Previous problem]] | ||
| + | * [[1985 AIME Problems/Problem 10 | Next problem]] | ||
* [[1985 AIME Problems]] | * [[1985 AIME Problems]] | ||
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| + | [[Category:Intermediate Geometry Problems]] | ||
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| + | [[Category:Intermediate Trigonometry Problems]] | ||
Revision as of 15:34, 19 November 2006
Problem
In a circle, parallel chords of lengths 2, 3, and 4 determine central angles of 
, 
, and 
radians, respectively, where 
. If 
, which is a positive rational number, is expressed as a fraction in lowest terms, what is the sum of its numerator and denominator?
Solution
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