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. More info can be found here: https://en.wikipedia.org/wiki/Brocard_points and here: http://mathworld.wolfram.com/BrocardPoints.html.
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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 French mathematician [[Henri Brocard]].
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== Problems ==
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* [[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 $P$ in triangle $\triangle ABC$ such that $\angle PAB=\angle PCA=\angle PBC$. It is also the unique point $P$ inside $\triangle ABC$ such that the sum of the distances from $P$ to $A, B,$ and $C$ is a minimum. These points are named after French mathematician Henri Brocard.

Problems

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