Brocard point

The Brocard point of a triangle is the point $P$ in triangle $\triangle ABC$ such that $\angle PAB=\angle PCA=\angle PBC$ . It is also the unique point $P$ inside $\triangle ABC$ such that the sum of the distances from $P$ to $A, B,$ and $C$ is a minimum. These points are named after Henri Brocard (1845 – 1922), a French mathematician. More info can be found here: https://en.wikipedia.org/wiki/Brocard_points and here: http://mathworld.wolfram.com/BrocardPoints.html.

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Brocard point