Education Technology

How to Find the Center of a Circle Determined by Three Non-Collinear Points

Activity Overview

The activity demonstrates the geometric construction of the center of a circle determined by 3 non-collinear points using the TI-Nspire calculator. The activity along with the Problem 3 worksheet guides the novice user to perform the task using the TI-Nspire handheld. Several of the calculator tools and utilities are used in completing the activity to find the center and measure the radius of the circle. Problem 4 includes instruction for writing the equation of the circle.

Before the Activity

The user should be able to grab and drag on the TI-Nspire handheld. It would be helpful to do the construction of a center and measurement of radius as a paper/pencil exercise on graph paper as a warm-up for this activity.

During the Activity

The activity contains 4 problems. Problem 1 is an introduction to determining the center of a circle geometrically.

Problem 2 is a demo of the process for determining the coordinates of the center and measuring the radius of the circle determined by 3 non-collinear points.

Problem 3 allows the user to use the Nspire tools and utilities to do the activity as performed in Problem 2.

Problem 4 is instruction/review of how to write the equation of a circle given its center and radius. Some discussion of accuracy of reporting the center and radius is worthwhile.

AP Mathematics standards consider 3 places as sufficient accuracy rather than requiring exact values. If the determining points are well selected, accuracy is not an issue for "well behaved" centers and radii.

After the Activity

The instructor may want to compare and contrast algebraic methods that locate the center of a circle and calculate the radius as a distance function.