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Exterior angle at the vertex of a cyclic quadrilateral

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

1. If <ABC = α°, what can we say about
2. What circle property describes the relationship in question (1)?
3. What is the relationship between <ADC and <CDE?
4. How can we use the property in question (3) to prove that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle?

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