Education Technology

Circumcenter and Incenter

Published on 06/09/2008

Activity Overview

In this activity, students examine the location of the circumcenter and incenter for different triangles.

Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

  • TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
  • TI-Navigator™  "send to class" feature
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 23 - 25 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Construct an acute triangle and label its vertices
  • Construct perpendicular bisectors of each side and observe that all perpendicular bisectors intersect in only one point
  • Determine the location of the circumcenter (the intersection point of the perpendicular bisectors)
  • Note that when the triangle is acute, the circumcenter lies inside the circle
  • Alter the triangle to create an obtuse triangle
  • Observe that when the triangle is obtuse, the circumcenter lies outside the circle
  • Alter the triangle to create a right triangle
  • Note that if a triangle is right, the circumcenter lies on the triangle


  • Create an acute triangle and construct angle bisectors of each angle
  • Observe that the angle bisectors of a triangle have only one point of intersection called the incenter
  • Determine the location of the incenter
  • Note that when the triangle is acute, the incenter lies inside the circle
  • Alter the triangle to create an obtuse triangle
  • Determine the location of the incenter
  • Alter the triangle to create a right triangle
  • Determine the location of the incenter
  • Note that for acute triangles, obtuse triangles, and right triangles, the incenter lies inside the triangle
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary