Question

using a compass and straight edge, construct a hexagon inscribed in a circle.

which of the following steps did you include in your construction?

• i drew a circle with diameter mon.
• i constructed two arcs: one with center at m and one with center at n.
• i marked the points where the arcs intersected the circle.
• i connected all four of these points of intersection and points m and n to form a regular hexagon.

Explanation:

Analyze the construction of an inscribed regular hexagon

1. A standard method to construct an inscribed regular hexagon using a diameter \(MON\) of a circle with center \(O\) involves:

• Drawing a circle with diameter \(MON\).
• Constructing two arcs with the same radius as the circle: one centered at \(M\) and one centered at \(N\).
• Marking the four points where these arcs intersect the circle.
• Connecting these four intersection points along with the diameter endpoints \(M\) and \(N\) to form the six vertices of the regular hexagon.

Evaluate the given options

1. All four statements describe the sequential steps of this specific construction method:

• "I drew a circle with diameter \(MON\)." (Step 1)
• "I constructed two arcs: one with center at \(M\) and one with center at \(N\)." (Step 2)
• "I marked the points where the arcs intersected the circle." (Step 3)
• "I connected all four of these points of intersection and points \(M\) and \(N\) to form a regular hexagon." (Step 4)

Determine the correct choices

1. Since all listed steps are correct and necessary parts of this standard construction process, all four checkboxes should be selected.

Answer:

• [x] I drew a circle with diameter MON. (Correct answer)
• [x] I constructed two arcs: one with center at M and one with center at N. (Correct answer)
• [x] I marked the points where the arcs intersected the circle. (Correct answer)
• [x] I connected all four of these points of intersection and points M and N to form a regular hexagon. (Correct answer)