Brocard points of a triangle | plane geometry | intermediate level

Episode 117.

Brocard points of a triangle | plane geometry | intermediate level.

Branch of mathematics: plane geometry.
Difficulty level: intermediate.

Theorem 1. For any triangle $ABC$, there exists a unique point $P$ such that $\angle{BAP}=\angle{CBP}=\angle{ACP}$. (This point $P$ is called the first Brocard point of the triangle $ABC$.)

Theorem 2. For any triangle $ABC$, there exists a unique point $Q$ such that $\angle{ABQ}=\angle{BCQ}=\angle{CAQ}$. (This point $Q$ is called the second Brocard point of the triangle $ABC$.)

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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