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See also the animated 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 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.|