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Equal chords in a circle

In the diagram, ED and GH are equal chords. Investigate the properties for equal chords in a circle by moving the sliders and clicking and dragging either of the blue points. What do you observe?

1. Why is OD = OE = OG = OH?
2. Given that ED and GH are equal chords, what test for congruent triangles will prove that triangles DOE and GOH are congruent?
3. How can we use the result in (2) to prove the properties for equal chords in a circle?

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