Bisected Chord

A chord is any line segment where the end points of the line are on the same circle. Click here to see more on chords. A segment bisector divides a line into two pieces with equal length. A perpendicular bisector is a bisector that is perpendicular to the segment it bisects.

Construction of a Bisected Chord

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This figure is constructed given any circle with a radius greater than zero, and two different points on the circle.

  1. Label the center of the circle O, and the points on the circle A and B. Connect A and B with a line segment.
  2. Draw the perpendicular bisector of AB. Label the points where this bisector intersects the circle C and D.
  3. Draw line segments CA, CB, DA, and DB.
  4. The figure is complete.


Change the figure by clicking and dragging points A, B, and O. What changes? What seems to stay the same? Write down three things that change when you move the points, and three things that seem to stay the same that are different from the givens in the paragraph above.

How could you prove mathematically the things that stay the same? Write a proof for one of the things that stay the same. Take a blank sheet of paper. Draw the figure at the top of the paper. Now make a table with two columns labeled 'Conclusion' and 'Reason'. Start with what you know (the givens), then draw each conclusion based on one of Euclid's axioms or postulates. To see Euclid's axioms and postulates, click here.

When you have gone as far as you can with your proof, trade proofs with your partner. Verify your partner's proof while your partner verifies your proof. Write any problems you find on the paper. If your partner has not finished the proof, try to finish it for your partner. When you both are done, talk together about what worked in each others proof and what didn't work.