To inscribe a regular hexagon in a circle, precise steps need to be followed. Let’s examine the given instructions:
1. Step 1 states: "Set the compass width to the diameter of the circle."
- An error is present in this step. To inscribe a regular hexagon, the compass width should not be the diameter of the circle. Instead, it should be set to the radius of the circle. The reason is that the side length of a regular hexagon inscribed in a circle is equal to the radius of the circle.
2. Step 2 instructs: "Place the fixed part of the compass on point B, and draw an arc that intersects the circle."
- This step is correct. When the compass width is set to the radius, placing the compass at any point on the circle and drawing arcs will correctly outline the vertices of the hexagon.
3. Step 3 states: "Move the fixed part of the compass to the point of intersection, and draw another arc that intersects the circle."
- This step is also correct as is. Moving the compass to the new intersection points sequentially and drawing arcs will successfully mark all the vertices of the hexagon.
4. Step 4 instructs: "Repeat step 3 three more times."
- This step is also logically consistent. After drawing the first arc, repeating the process three more times (a total of four movements, added to the initial point) would leave two more movements to complete the hexagon, summing up to exactly six sides.
5. Step 5 instructs: "Connect the points of intersection to complete the hexagon."
- This step is accurate. Connecting the points where the arcs intersect the circle will form the hexagon.
Hence, the error is in Step 1, and it should be revised. The corrected step should say:
A. In step 1, the compass width should be set to the length of the radius of the circle.
