Difference between revisions of "Brocard point"
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| − | The '''Brocard point''' of a [[triangle]] is the point <math>P</math> in triangle <math>\triangle ABC</math> such that <math>\angle PAB=\angle PCA=\angle PBC</math>. It is also the unique point <math>P</math> inside <math>\triangle ABC</math> such that the sum of the distances from <math>P</math> to <math>A, B,</math> and <math>C</math> is a minimum. These points are named after | + | The '''Brocard point''' of a [[triangle]] is the point <math>P</math> in triangle <math>\triangle ABC</math> such that <math>\angle PAB=\angle PCA=\angle PBC</math>. It is also the unique point <math>P</math> inside <math>\triangle ABC</math> such that the sum of the distances from <math>P</math> to <math>A, B,</math> and <math>C</math> is a minimum. These points are named after French mathematician [[Henri Brocard]]. |
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| + | == Problems == | ||
| + | * [[1999_AIME_Problems/Problem_14]] | ||
| + | [[Category:Geometry]] | ||
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Latest revision as of 21:33, 19 February 2025
The Brocard point of a triangle is the point 
in triangle 
such that 
. It is also the unique point inside such that the sum of the distances from to 
and 
is a minimum. These points are named after French mathematician Henri Brocard.
Problems
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