Napoleon's theorem | plane geometry | intermediate level

Episode 113.

Napoleon's theorem | plane geometry | intermediate level.

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

Theorem 1. Let $ABC$ be a triangle. Let $BCP$, $CAQ$, $ABR$ be equilateral triangles constructed on the sides of the triangle $ABC$ to the outside. Let $X$, $Y$, $Z$ be the centers of these equilateral triangles respectively. Then the triangle $XYZ$ is itself equilateral.

Theorem 2. Let $ABC$ be a triangle. Let $BCP'$, $CAQ'$, $ABR'$ be equilateral triangles constructed on the sides of the triangle $ABC$ to the inside. Let $X'$, $Y'$, $Z'$ be the centers of these equilateral triangles respectively. Then the triangle $X'Y'Z'$ is itself equilateral.

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

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