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Opposite angles of a cyclic quadrilateral

Investigate the circle property by clicking and dragging any of the blue points. What observation can you make regarding the opposite angles of a cyclic quadrilateral? Confirm your conjecture by revealing the relevant measurements then show the property.

1. If <ABC = α°, what is the size of <AOC?
2. If <ADC = β°, what is the size of the reflex <AOC?
3. What is the sum of the <AOC and the reflex <AOC?
4. How can we use the result from question (3) to prove this circle property?

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