Definition:Brocard Angle

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

• Definition:Brocard Points
• Brocard Angle is Unique

• Yff's Conjecture

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