Define the first Brocard Point as the interior point of a Triangle for which the Angles , , and are equal. Similarly, define the second Brocard Point as the interior point for which the Angles , , and are equal. Then the Angles in both cases are equal, and this angle is called the Brocard angle, denoted .

The Brocard angle of a Triangle is given by the formulas

(1) | |||

(2) | |||

(3) | |||

(4) | |||

(5) | |||

(6) | |||

(7) |

where is the Triangle Area, , , and are Angles, and , , and are side lengths.

If an Angle of a Triangle is given, the maximum possible Brocard angle is given by

(8) |

(9) |

(10) |

(11) |

**References**

Abi-Khuzam, F. ``Proof of Yff's Conjecture on the Brocard Angle of a Triangle.'' *Elem. Math.* **29**, 141-142, 1974.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, pp. 263-286 and 289-294, 1929.

Le Lionnais, F. *Les nombres remarquables.* Paris: Hermann, p. 28, 1983.

© 1996-9

1999-05-26