Question

Mai wants to construct a regular hexagon inscribed in the circle centered at C. Will these instructions work to finish the hexagon from the construction given? If so, explain why Mai is correct. If not, explain how you would finish the construction correctly.

i. Draw the circle centered at D with radius CD.
ii. Mark the intersection of the circle with the circle centered at C, and label that point E.
iii. Draw the circle centered at E with radius DE.
iv. Mark the intersection of the circle with the circle centered at D, and label that point F.
v. Connect ABCDEF to make a regular hexagon.​

Answer 1

The given instructions are incomplete for creating a regular hexagon; a correct method involves stepping off the radius of the circle to each vertex, ensuring all sides and interior angles are equal.

Tat

Step-by-step explanation:

The instructions provided by Mai to construct a regular hexagon inscribed in a circle are not complete. Drawing a circle centered at D with radius CD and marking the intersection of this circle with the circle centered at C may give the point E. However, repeating the same step from E may not result in a regular hexagon because these instructions do not guarantee that all sides of the hexagon will be equal or that each interior angle will be 120 degrees.

To correctly construct a regular hexagon, Mai could use the fact that the central angle between two consecutive vertices of a regular hexagon inscribed in a circle is 60 degrees (since a hexagon has 6 sides, and the total measure of angles around a point is 360 degrees, so 360/6 = 60). Therefore, after drawing the initial circle centered at C, Mai could:

1. Draw a radius from C to any point A on the circle.
2. Using a compass set to the length of the radius, step off this distance along the circumference of the circle five more times to find the remaining vertices B, D, E, F, and G.
3. Finally, connect these points to form the regular hexagon ABCDEFG.

Answer 2

Place your compass point on the paper and draw a circle. (Keep this compass span!)

2. Place a dot, labeled P, anywhere on the circumference of the circle to act as a starting point.

3. Without changing the span on the compass, place the compass point on P and swing a small arc crossing the circumference of the circle.

4. Without changing the span on the compass, move the compass point to the intersection of the previous arc and the circumference and make another small arc on the circumference of the circle.

5. Keep repeating this process of "stepping" around the circle until you return to point P.

6. Starting at P, connect to each arc on the circle forming the regular hexagon.