Let $AC$ be a line segment in the plane and $B$ a point between $A$ and $C$. Construct isosceles triangles $PAB$ and $QBC$ on one side of the segment $AC$ such that $\angle{APB} =\angle{BQC}= 120^o$ and an isosceles triangle RAC on the otherside of AC such that $\angle{ARC} = 120^o$. Show that $PQR$ is an equilateral triangle.
I saw this question on https://artofproblemsolving.com/community/c6h57976p355627 And someone commented this:
Isn't this just Napoleon's theorem, except the triangle is degenerate (the one relating to the first fermat point?)
Others agreed with him, now I'm curious what this means.