Perpendicular bisectors and circumcenter of a triangle

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Circumcentre for different types of triangles is investigated with this activity and this further explores several geometric relationships related to the circumcentre and perpendicular bisectors.

Objectives

Introduce perpendicular bisectors in a triangle and their point of concurrence.

Estimated Time

30 minutes.

Prerequisites/Instructions, prior preparations, if any

Ensure that circles, triangles, perpendicular bisectors and their constructions are covered

Materials/ Resources needed

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

Geogebra files: Concurrency of perpendicular bisectors.ggb


Download this geogebra file from this link.


Process (How to do the activity)

  1. Project the geogebra file and ask the following questions.
  • Developmental Questions:
  1. What is a perpendicular bisector ?
  2. How do you construct it ?
  3. Identify the point of intersection of perpendicular bisectors in different triangles.
  4. What is circumcircle ?
  • Evaluation:
  1. How is circumradius determined ?
  2. What parts of the circle is circumcircle touching ?
  • Question Corner:
  1. What are the practical applications of determining the circumcircle ?