Perpendicular bisectors and circumcenter of a triangle

The perpendicular bisectors of the three sides of a triangle are concurrent in a point that is equidistant (the same distance) from the vertices of the triangle. Unlike the centroid, the circumcenter is not always located inside the triangle. The location of the circumcenter depends on the type of triangle that we have.

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: This eogebra file was done by ITfC-Edu-Team.

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 ?