Difference between revisions of "1999 AIME Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | 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 == | ||
| + | * [[1999_AIME_Problems/Problem_13|Previous Problem]] | ||
| + | * [[1999_AIME_Problems/Problem_15|Next Problem]] | ||
* [[1999 AIME Problems]] | * [[1999 AIME Problems]] | ||
Revision as of 02:12, 22 January 2007
Problem
Point 
is located inside traingle 
so that angles 
and 
are all congruent. The sides of the triangle have lengths 
and 
and the tangent of angle 
is 
where 
and 
are relatively prime positive integers. Find 
