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.