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Draw a chord between two points. Use a compass to draw two overlapping circles. Draw a vertical line through the two points at which the circles intersect. Erase the two overlapping circles. Sketch two new circles. Draw a line through the points at which these new circles intersect. Find the center.
Use a ruler or straightedge to draw a straight line inside the circle, from one edge to another. The points that you use don't matter. Label the two points A and B. The circles should be the exact same size. Make A the center of one circle, and B the center of the other. Space the two circles so that they overlap like a Venn diagram. Draw these circles in pencil, not pen. The process will be simpler if you are able to erase these circles later on. There will be a point at the top and a point at the bottom of the "Venn diagram" space created between the overlap of the circles. Use a ruler to make sure that the line protrudes straight through these points. Finally, label the two points (C and D) at which this new line crosses the rim of the original circle. This line marks the diameter of the original circle. This should clear up your work space for the next step of the process. Now, you should have a circle with two perpendicular lines running through it. Do not erase the center points (A and B) of these circles! You will be drawing two new circles. Use your compass to draw two equal circles: one with the point C at its center, and one with the point D. These circles, too, should overlap like a Venn diagram. Remember: C and D are the points at which the vertical line intersects the main circle. This straight, horizontal line should cut through the overlap space of the two new circles. This line is the second diameter of your original circle, and it should be exactly perpendicular to the first diameter line. The intersection point of the two straight diameter lines is the exact center of the circle! Mark this center point for reference. If you want to clean up the page, feel free to erase the diameter lines and the non-original circles.