Hexagon inscribed in a circle
Geometry construction using a compass and straightedge
This page shows how to construct (draw) a
inscribed in a circle with a compass and straightedge or ruler. This is the largest hexagon that will fit in the circle, with each
touching the circle. Ina regular hexagon, the side length is equal to the distance from the center to a vertex, so we use this fact to set the compass to the proper side length, then step around the circle marking off the vertices.
Printable step-by-step instructions
The above animation is available as a
printable step-by-step instruction sheet, which can be used for making handouts
or when a computer is not available.
Explanation of method
As can be seen in Definition of a Hexagon,
each side of a regular hexagon is equal to the distance from the center to any vertex.
This construction simply sets the compass width to that radius, and then steps that length off around the circle
to create the six vertices of the hexagon.
Try it yourself
Click here for a printable worksheet containing two problems to try.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Constructions pages on this site
Circles, Arcs and Ellipses
(C) 2009 Copyright Math Open Reference. All rights reserved
Math Open Reference now has a Common Core alignment.
See which resources are available on this site for each element of the Common Core standards.
Check it out