The Geometer´s warehouse


Back to home

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?