Definition:Brocard Angle
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Definition
Let $\triangle ABC$ be a triangle such that $A \to B \to C \to A$ travels anticlockwise around $\triangle ABC$.
Let $P$ and $Q$ be the first and second Brocard points of $\triangle ABC$ respectively.
Let:
\(\ds \omega\) | \(=\) | \(\ds \angle PAB = \angle PBC = \angle PCA\) | ||||||||||||
\(\ds \omega'\) | \(=\) | \(\ds \angle QAC = \angle QCB = \angle QBA\) |
From Brocard Angle is Unique:
- $\omega = \omega'$
This angle $\omega = \omega'$ is the Brocard angle of $\triangle ABC$.
Also see
Source of Name
This entry was named for Pierre René Jean Baptiste Henri Brocard.
Sources
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $0,56559 56245 \ldots$
- Weisstein, Eric W. "Brocard Angle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrocardAngle.html