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 01:12, 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