Go directly to content
Search site >



Regular pentagon 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.
1.  Draw a diameter of the circle through the center point and mark its endpoints C and M. It does not have to be vertical.

2.  Construct a perpendicular to CM at the point O.

For more on this see Constructing a perpendicular at a point on a line.

3.   Mark the point S where it crosses the circle.

4.   Find the midpoint L of the segment SO by constructing its perpendicular bisector.

For more on this see Constructing the perpendicular bisector of a line segment.

5.  Set the compass on L, adjust its width to S or O, and draw a circle.
6.   Draw a line from M, through L so it crosses the small circle in two places. Label them N and P.
7.   Set the compass on M and adjust its width to P.
8.   Draw a broad arc that crosses the given circle in two places. Label them A and E.
9.   Set the compass on M and adjust its width to N.
10.   Draw a broad arc that crosses the given circle in two places. Label them B and D.
11.   Draw a line from A to B, then B to C etc, until you have drawn all five sides of the pentagon.
Done.   ABCDE is a regular pentagon inscribed in the given circle.
Try it yourself
Click here for a printable worksheet containing 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