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G.G.49 Investigate, justify, and apply theorems regarding chords of a circle:
the relative lengths of chords as compared to their distance from the center of the circle
Lesson Launcher Objectives:
Discover that the relative length of a chord of a circle can be determined by its distance from the center .
Discover that the longest chord of a circle must pass through the center of the circle and therefore is the diameter.
Procedure:
The student opens Cabri Jr. and the APPVAR CHORDS2
As As the student explores the figure by moving various points they will be able to conclude that as the distance from the center decreases/increases the length of the chord increases/decreases.
Select, grab and drag point A or point B. What happens to the length of OX as the length of AB increases? The length of OX decreases
Select, grab and drag point A or point B. What happens to the length of OX as the length of AB decreases? The length of OX increases
Select, grab and drag point C or point D. What happens to the length of OY as the length of CD increases? The length of OY decreases
Select, grab and drag point C or point D. What happens to the length of OY as the length of CD decreases? The length of OY increases
5.) In circle O chords PQ and RS are drawn and chord PQ is closer to point O than
chord RS. What can you conclude about the lengths of O chord PQ and chord RS?
PQ > RS
6.) What is the longest chord in a circle? The diameter
7.) How far from the center is the longest chord you can draw in a circle? Since it is a diameter it passes through the center therefore is 0 units from the center.
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