Education Technology

# Activities

• ##### Subject Area

• Math: Geometry: Circles

9-12

30 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.0

## Chords and Circles

#### Activity Overview

Students will begin this activity by exploring how the chord in a circle is related to its perpendicular bisector. Investigation will include measuring lengths and distances from the center of the circle. These measurements will then be transferred to a graph to see the locus of the intersection point of the measurements as the endpoint of a chord is moved around the circle. In the extension, students will be asked to find an equation for the ellipse that models the relationship.

#### Key Steps

• On page 1.3, students are given a circle A where point D is the midpoint of a chord BC. As they drag point B around the circle, they should observe that the perpendicular bisector of BC always passes through the center of the circle.  Students should explain why this is so.