Pentagon inscribed in a circle

Pentagon inscribed in a circle

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 straight edge.        

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.  

   

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

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

         

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.   

Now the ABCDE is a regular pentagon by inscribed in the given circle is  done.

 

Composed by:  R.Satheesh, M.E., Asst Prof., email: rsatheeshemail@gmail.com.