# Constructing a pentagon inscribed in a circle

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After doing this Your work should look like this

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 compasses 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 compasses 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 compasses 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

### Non-Euclidean constructions

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