Brocard Points are Isogonal Conjugates

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Theorem

The first and second Brocard Points are Isogonal Conjugates.

Proof

Let the point $P$ be first Brocard point of $\triangle ABC$.

Then

$\angle PAB = \angle PBC = \angle PCA=\omega$

Let the point $Q$ be second Brocard point of $\triangle ABC$.

Then

$\angle QAC = \angle QCB = \angle QBA=\omega'$

To prove $P,Q$ are Isogonal Conjugates, it suffices to prove $\omega=\omega'$.

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