Difference between revisions of "1989 AIME Problems/Problem 9"
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== Problem == | == Problem == | ||
+ | Let <math>a_{}^{}</math>, <math>b_{}^{}</math>, <math>c_{}^{}</math> be the three sides of a triangle, and let <math>\alpha_{}^{}</math>, <math>\beta_{}^{}</math>, <math>\gamma_{}^{}</math>, be the angles opposite them. If <math>a^2+b^2=1989^{}_{}c^2</math>, find | ||
+ | <center><math>\frac{\cot \gamma}{\cot \alpha+\cot \beta}</math></center> | ||
== Solution == | == Solution == | ||
+ | {{solution}} | ||
== See also == | == See also == | ||
+ | * [[1989 AIME Problems/Problem 10|Next Problem]] | ||
+ | * [[1989 AIME Problems/Problem 8|Previous Problem]] | ||
* [[1989 AIME Problems]] | * [[1989 AIME Problems]] |
Revision as of 23:09, 24 February 2007
Problem
Let ,
,
be the three sides of a triangle, and let
,
,
, be the angles opposite them. If
, find
![$\frac{\cot \gamma}{\cot \alpha+\cot \beta}$](http://latex.artofproblemsolving.com/8/5/8/858c49b569dc76c503dbdbfa8d0b78fd2c04fe1d.png)
Solution
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