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Perpendicular from the centre of a circle to 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 perpendicular from the centre of a circle to a chord?

1. Why is OA = OB?
2. Given that <OCA = <OCB = 90° (OC ⊥ 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 (2) to prove that the perpendicular from the centre of a circle to a chord bisects the chord?

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