Difference between revisions of "1992 AIME Problems/Problem 14"

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== See also ==
 
== See also ==
* [[1992 AIME Problems/Problem 13 | Previous Problem]]
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{{AIME box|year=1992|num-b=13|num-a=15}}
  
* [[1992 AIME Problems/Problem 15 | Next Problem]]
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[[Category:Intermediate Geometry Problems]]
 
 
* [[1992 AIME Problems]]
 

Revision as of 16:04, 11 March 2007

Problem

In triangle $ABC^{}_{}$, $\displaystyle A'$, $\displaystyle B'$, and $\displaystyle C'$ are on the sides $\displaystyle BC$, $AC^{}_{}$, and $AB^{}_{}$, respectively. Given that $\displaystyle AA'$, $\displaystyle BB'$, and $\displaystyle CC'$ are concurrent at the point $O^{}_{}$, and that $\frac{AO^{}_{}}{OA'}+\frac{BO}{OB'}+\frac{CO}{OC'}=92$, find $\frac{AO}{OA'}\cdot \frac{BO}{OB'}\cdot \frac{CO}{OC'}$.

Solution

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See also

1992 AIME (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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All AIME Problems and Solutions