# Activities

• • • ##### Subject Area

• Math: Geometry: Analytic Geometry
• Math: Geometry: Circles

• ##### Author 9-12

50 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

None
• ##### Report an Issue

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.