Inscribing Regular Hexagon in Circle/Porism

Proof
In the same way as for the regular pentagon, we can draw tangents to the circle at the vertices of the regular hexagon.

This will draw a regular hexagon which has been circumscribed about the circle.

Further, in a similar way to methods used for the regular pentagon, a circle can be inscribed in a regular hexagon and circumscribed about a regular hexagon.