Brocard

Pierre René Jean Baptiste Henri Brocard

Born: 12 May 1845 in Vignot, France
Died: 16 Jan 1922 in Bar-le-Duc, France

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Henri Brocard was a French army officer who studied meteorology but is best remembered for his work on the triangle. The Brocard points of a triangle ABC are O, O' where OAB, OBC and OCA and the angles O'BA, O'CB and O'AC are equal. [Draw a circle tangent to AB at A passing through C, another tangent to BC at B passing through A, a third tangent to CA at C passing through B. They are concurrent at O.] Angle OAB is called the Brocard angle and satisfies cot OAB = cot A + cot B + cot C.

References:

  1. Dictionary of Scientific Biography
  2. L Guggenbuhl, Henri Brocard and the Geometry of the triangle, Mathematical Gazette 32 (1953), 241-243. 
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JOC/EFR February 1996