This activity is intended to supplement Geometry, Chapter 9, Lesson 3.
When hikers and skiers go into terrain where there is a risk of avalanches, they take safety equipment including avalanche rescue beacons. An avalanche rescue beacon sends and receives electromagnetic field signals that can travel up to about 30 meters. The search pattern used to locate a beacon buried in the snow is based on the properties of chords and diameters in circles.
Problem 1 – Relationship between a chord an its perpendicular bisector
1. Open Cabri Jr. and construct a circle to represent the beacon signal. Hide the center of the circle.
8. The rescuer walks back to the midpoint of this new path.
Problem 2 – Extension
10. Write a proof of the relationship used in the activity. Given a chord of a circle and its perpendicular bisector, prove that the perpendicular bisector passes through the center of the circle.
11. Use a compass and straightedge to construct a circle and a chord. Construct the perpendicular bisector of the chord and see that it passes through the center of the circle.