
How to construct a hexagon, a regular 6sided polygon, inscribed in a given circle?

1. 
 Start with the given circle.


2. 
 Use the
construction of the horizontal and vertical centerlines to create these lines.


3. 
 Draw an arc with its center at the endpoint of the horizontal centerline on the right, and passing through the intersection of both centerlines 2 (and therefore passing through the center of circle 1). The arc must intersect circle 1 twice.


4. 
 Draw the connection between the endpoint of the horizontal centerline on the right and the upper intersection of arc 3 and circle 1.


5. 
 Repeat this for the lower intersection.


6. 
 Repeat step 3 for the endpoint on the left.


7. 
 Repeat step 4 for the endpoint on the left and the upper intersection of arc 6 and circle 1.


8. 
 Repeat step 7 for the lower intersection.


9. 
 Draw the connection between the upper endpoints of line segments 4 and 7.


10. 
 Draw the connection between the lower endpoints of line segments 5 and 8.


11. 
 Line segments 4, 5, 7, 8, 9 and 10 together form the hexagon to be constructed.

