Question

What are the steps for using a compass and straightedge to construct a regular hexagon inscribed in a circle?

Answer 1

The steps to construct a regular hexagon inscribed in a circle using a compass and straightedge are given as follows:

1. Construct a circle with its center at point H.

2. Construct horizontal line l and point H on line l

3. Label the point of intersection of the circle and line l to the left of point H, point J, and label the point of intersection of the circle and line l to the right of point H, point K.

4. Construct a circle with its center at point J and having radius ​ HJ ​ . Construct a circle with its center at point K having radius ​ HJ

5. Label the point of intersection of circles H and J that lies above line l, point M, and the point of their intersection that lies below line l, point N. Label the point of intersection of circles H and K that lies above line l, point O, and the point of their intersection that lies below line l, point P.

6. Construct and JM⎯⎯⎯⎯⎯, MO⎯⎯⎯⎯⎯⎯⎯, OK⎯⎯⎯⎯⎯⎯⎯, KP⎯⎯⎯⎯⎯, PN⎯⎯⎯⎯⎯⎯, and NJ⎯⎯⎯⎯⎯ to complete regular hexagon JMOKPN .