# Activities

• • • ##### Subject Area

• Math: Geometry: Circles

• ##### Author 9-12

30 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Other Materials
Student Activity Hand Out
• ##### Report an Issue

Cabri Jr. Perpendicular Bisector of a Circle

#### Activity Overview

This activity uses Cabri™ Jr. to discover that the perpendicular of a chord passes through the centre of a circle.

#### Before the Activity

Students require the activity handout.

#### During the Activity

1. Draw a circle in the center of the screen. Label the center O. 2. Draw two points that are on the circle. Label the points A and B. Use the Segment tool to construct a chord, AB, connecting the two points.See Figure 1. 3. Construct a perpendicular bisector to AB. Use the Point Intersection tool to construct a point at the intersection of the chord and the perpendicular bisector. Label the point C. See Figure 3. 4. Grab point B and move it to a new location on the circle.

• Use the measure tool to measure the length of segment AC and BC.
• 5. Draw a new chord on the circle. Construct the perpendicular bisector for the new chord.
• Make a conjecture about the relationship between the perpendicular bisector of a chord and the centre of the circle. Test the conjecture by dragging any of the endpoints of the chords to a new location on the circle.
• 6. Use the Segment Tool to construct a radius of the circle to point A. Use the Measure Tool to measure the length of the sides of the triangle. See Figure 6. ? Use the Pythagorean Theorem and your measurements to verify triangle ACO is a right angle triangle.

#### After the Activity

Go over answers to Student hand out. Reteach as necessary.