1. Begin with a circle, but no center point. 

2. Draw chord AB. 

3. Construct the perpendicular bisector of chord AB. Let C and D be the points where it intersects the circle. (Refer to the construction of a perpendicular bisector.) 

4. Chord CD is a diameter of the circle. Construct point P, the midpoint of diameter CD. Point P is the center point of the circle. (Refer to the construction of a the midpoint of a line segment.) 
