Cyclic quadrilateral

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A quadrilateral ABCD is called cyclic if all four vertices of it lie on a circle.In a cyclic quadrilateral the sum of opposite interior angles is 180 degrees.If the sum of a pair of opposite angles of a quadrilateral is 180, the quadrilateral is cyclic.In a cyclic quadrilateral the exterior angle is equal to interior opposite angle.


Understanding cyclic quadrilaterals

Relation between angles of a cyclic quadrilateral.

Estimated Time

10 minutes

Prerequisites/Instructions, prior preparations, if any

Circle and quadrilaterals should have been introduced.

Materials/ Resources needed

Digital : Laptop, geogebra file, projector and a pointer.

Geogebra file: Cyclic quadrilateral.ggb

Download this geogebra file from this link.

Process (How to do the activity)

  1. The teacher can recall the concept of a circle, quadrilateral, circumcircle.
  2. Can explain a cyclic quadrilateral and show the geogebra applet.
  3. Move points, the vertices of the quadrilateral and let the students observe the sum of opposite interior angles.
  • Developmental Questions:
  1. What two figures do you see in the figure ?
  2. Name the vertices of the quadrilateral.
  3. Where are all the 4 vertices situated ?
  4. Name the opposite interior angles of the quadrilateral.
  5. What do you observe about them.
  • Evaluation:
  1. Compare the cyclic quadrilateral to circumcircle.
  • Question Corner
  1. Can all quadrilaterals be cyclic ?
  2. What are the necessary conditions for a quadrilateral to be cyclic ?