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Hexagon inscribed in a circle
Geometry construction using a compass and straightedge
Step-by-step Instructions Printer friendly version
After doing this Your work should look like this
We start with the given circle, center O.

Note: If you are not given the center, you can find it using the method shown in Finding the center of a circle with compass and straightedge.		 Geometry construction with compass and straightedge or ruler or ruler
1.  Mark a point anywhere on the circle. This will be the first vertex of the hexagon.
2.  Set the compass on this point and set the width of the compass to the center of the circle. The compass is now set to the radius of the circle
3.  Make an arc across the circle. This will be the next vertex of the hexagon.

(It turns out that the side length of a hexagon is equal to its circumradius - the distance from the center to a vertex).
4.  Move the compass on to the next vertex and draw another arc. This is the third vertex of the hexagon.
5.  Continue in this way until you have all six vertices.
6.   Draw a line between each successive pairs of vertices, for a total of six lines.
6.   Done. These lines form a regular hexagon inscribed in the given circle.  

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

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions

(C) 2009 Copyright John Page