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>. | + | 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]]. |
− | + | == Problems == | |
+ | * [[1999_AIME_Problems/Problem_14]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
+ | {{stub}} |
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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