Which statement is not a step used when constructing an inscribed hexagon? swing two arcs above and below the radius. keep your compass at the width equal to the radius of the circle. place the compass on the point where the circle and radius intersect. swing an arc the length of the radius from the point on the circle.

Final answer:

The incorrect step when constructing an inscribed hexagon is 'swing two arcs above and below the radius'. When constructing an inscribed hexagon, you sequentially position the compass along the circle's circumference, maintaining the same compass width (equivalent to the circle's radius), and draw intersecting arcs.

Explanation:

The step which is not used when constructing an inscribed hexagon is to 'swing two arcs above and below the radius'. All the other steps mentioned are correct and are part of the process in creating an inscribed hexagon in a circle. Here's the correct sequence of actions:

1. Draw a circle using a compass.
2. Place the point of your compass at any location on the circle's boundary to define a starting point.
3. Maintaining the same compass width (radius of the circle), create additional points on the circle's edge by consecutively placing the compass' point on the previous point and swinging an arc that intersects with the circumference of the circle.
4. Repeat this procedure until six points are established around the circumference of the circle.
5. Finally, connect these six points to make the hexagon.

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Final answer:

The statement 'swing an arc the length of the radius from the point on the circle' is not a step used when constructing an inscribed hexagon because it would extend beyond the circle and not aid in creating equal divisions. Option D is correct.

Explanation:

The process of constructing an inscribed hexagon involves dividing a circle into six equal arcs using a compass and a straightedge. The statements A, B, and C are accurate descriptions of steps used in this process. Statement A references the actions of swinging two arcs above and below the radius, which helps establish equal divisions around the circle.

Statement B suggests keeping the compass width equal to the radius of the circle, an important step in ensuring consistent arc sizes. Statement C mentions placing the compass on the point where the circle radius intersects.

However, statement D, swing an arc the length of the radius from the point on the circle, is not a step used in the construction of an inscribed hexagon. This action would result in a distance that extends beyond the circle, and would not aid in creating equal divisions needed for an inscribed hexagon.

Option D is correct.

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