Napoleon's Theorem

Theorem
Let $\triangle ABC$ be an arbitrary triangle.

Let $\triangle ABF$, $\triangle BCD$ and $\triangle ACE$ be equilateral triangles constructed on $AB$, $BC$ and $AC$ respectively on the exterior of $\triangle ABC$.

Let $O_1$, $O_2$ and $O_3$ be the incenters of $\triangle ABF$, $\triangle BCD$ and $\triangle ACE$.

Then $\triangle O_1 O_2 O_3$ is an equilateral triangle.


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