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 Henri Brocard (1845 – 1922), a French mathematician. | + | 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 Henri Brocard (1845 – 1922), a French mathematician. https://en.wikipedia.org/wiki/Brocard_points and here: http://mathworld.wolfram.com/BrocardPoints.html. |
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| + | Example problem: [[1999_AIME_Problems/Problem_14]] | ||
Latest revision as of 20:13, 27 January 2024
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 Henri Brocard (1845 – 1922), a French mathematician. https://en.wikipedia.org/wiki/Brocard_points and here: http://mathworld.wolfram.com/BrocardPoints.html.
Example problem: 1999_AIME_Problems/Problem_14
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