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Line from the centre to the midpoint of a chord

In the diagram, C is the midpoint of the chord AB. Change the shape and orientation of the diagram by clicking and dragging any of the blue points. What observations can you make about the line from the centre of the circle to the midpoint of the chord?

1. Why is OA = OB?
2. Given that AC = CB (C is the midpoint of AB) and OC is common to triangles OAC and OBC, what test for congruency will prove that the two triangles are congruent?
3. How can we use the result from question (2) to prove that the line from the centre of a circle to the midpoint of a chord is perpendicular to the chord?

© State of New South Wales, Department of Education, 2018