# Constructing a pentagon inscribed in a circle

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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. 