Difference between revisions of "1999 AIME Problems/Problem 14"

 
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== Problem ==
 
== Problem ==
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Point <math>\displaystyle P_{}</math> is located inside traingle <math>\displaystyle ABC</math> so that angles <math>\displaystyle PAB, PBC,</math> and <math>\displaystyle PCA</math> are all congruent.  The sides of the triangle have lengths <math>\displaystyle AB=13, BC=14,</math> and <math>\displaystyle CA=15,</math> and the tangent of angle <math>\displaystyle PAB</math> is <math>\displaystyle m/n,</math> where <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> are relatively prime positive integers.  Find <math>\displaystyle m+n.</math>
  
 
== Solution ==
 
== Solution ==
  
 
== See also ==
 
== See also ==
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* [[1999_AIME_Problems/Problem_13|Previous Problem]]
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* [[1999_AIME_Problems/Problem_15|Next Problem]]
 
* [[1999 AIME Problems]]
 
* [[1999 AIME Problems]]

Revision as of 01:12, 22 January 2007

Problem

Point $\displaystyle P_{}$ is located inside traingle $\displaystyle ABC$ so that angles $\displaystyle PAB, PBC,$ and $\displaystyle PCA$ are all congruent. The sides of the triangle have lengths $\displaystyle AB=13, BC=14,$ and $\displaystyle CA=15,$ and the tangent of angle $\displaystyle PAB$ is $\displaystyle m/n,$ where $\displaystyle m_{}$ and $\displaystyle n_{}$ are relatively prime positive integers. Find $\displaystyle m+n.$

Solution

See also