Constructing a pentagon inscribed in a circle

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.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy method)
• Parallel line through a point (rhombus method)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object