the hexagon is circumscribed about the circle
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No, the circle is inscribed in the quadrilateral.
An inscribed circle has its circumference tangent to each side of the square or other type of polygon surrounding it.
The length of on side of an equilateral hexagon is half the diameter of the circumscribing circle.
If you know the length of the side of the (regular) hexagon to be = a the radius r of the inscribed circle is: r = a sqrt(3)/2
The diameter of a regular hexagon is 1 side bigger than each side.