With aregularhexagon you have 6 isosceles triangles because the legs of the triangle are the radius of the circumcircle.

With aregularhexagon the central angle must be

An isosceles triangle with one interior angle of 60° must be an equilateral triangle because all interior angles are 60° and therefore all sides must have equal length.

And that's the reason why the circumference of a regular 6gon is