Difference between revisions of "1995 AIME Problems/Problem 9"

 
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== Problem ==
 
== Problem ==
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Triangle <math>\displaystyle ABC</math> is isosceles, with <math>\displaystyle AB=AC</math> and altitude <math>\displaystyle AM=11.</math>  Suppose that there is a point <math>\displaystyle D</math> on <math>\displaystyle \overline{AM}</math> with <math>\displaystyle AD=10</math> and <math>\displaystyle \angle BDC=3\angle BAC.</math>  Then the perimeter of <math>\displaystyle \triangle ABC</math> may be written in the form <math>\displaystyle a+\sqrt{b},</math> where <math>\displaystyle a</math> and <math>\displaystyle b</math> are integers.  Find <math>\displaystyle a+b.</math>
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[[Image:AIME_1995_Problem_9.png]]
  
 
== Solution ==
 
== Solution ==
  
 
== See also ==
 
== See also ==
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* [[1995_AIME_Problems/Problem_8|Previous Problem]]
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* [[1995_AIME_Problems/Problem_10|Next Problem]]
 
* [[1995 AIME Problems]]
 
* [[1995 AIME Problems]]

Revision as of 01:21, 22 January 2007

Problem

Triangle $\displaystyle ABC$ is isosceles, with $\displaystyle AB=AC$ and altitude $\displaystyle AM=11.$ Suppose that there is a point $\displaystyle D$ on $\displaystyle \overline{AM}$ with $\displaystyle AD=10$ and $\displaystyle \angle BDC=3\angle BAC.$ Then the perimeter of $\displaystyle \triangle ABC$ may be written in the form $\displaystyle a+\sqrt{b},$ where $\displaystyle a$ and $\displaystyle b$ are integers. Find $\displaystyle a+b.$

AIME 1995 Problem 9.png

Solution

See also

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