Symmetries of Chords of a Circle

Azean Khamis, Jul 26, 2020

Learning Goals: 1. Use GeoGebra to explore properties related to symmetries of chords of a circle. 2. Apply symmetric properties of chords of a circle to find lengths.

Table of Contents

  1. Property 1A
    1. PROPERTY 1A
  2. Property 1B
    1. PROPERTY 1B
  3. Property 2
    1. PROPERTY 2
  4. Challenge
    1. CHALLENGE

1.

Property 1A

  • 1. PROPERTY 1A

1.1.

PROPERTY 1A

APPLET
Draw a chord for circle A. Construct the perpendicular bisector of the chord. Move the chord, paying attention to the perpendicular bisector.
CONJECTURE:
The perpendicular bisector of a chord always goes through what point of the circle.
– Azean Khamis, Mark Humphries

2.

Property 1B

  • 1. PROPERTY 1B

2.1.

PROPERTY 1B

APPLET
Construct a diameter of the circle. Draw a chord such that it is perpendicular to the diameter. Find the lengths of each segment of the chord. Move the chord, paying attention to the lengths of each segment of the chord.
CONJECTURE:
If a diameter is perpendicular to a chord then the diameter will __________________. (complete the statement)
– Azean Khamis, Mark Humphries

3.

Property 2

  • 1. PROPERTY 2

3.1.

PROPERTY 2

APPLET
Find the length of each chord to the centre of the circle. Move the chords, paying attention to the length of each chord to the centre of the circle.
CONJECTURE:
If two chords of a circle are of the same length then what conclusion can we make?
EXTENSION:
In the applet above, measure arcs CD and FE. Move the chords, paying attention to the lengths of arcs CD and FE.[br][br]If two chords of a circle are of the same length, what other conclusion can you make?
– Azean Khamis, Mark Humphries

4.

Challenge

  • 1. CHALLENGE

4.1.

CHALLENGE

APPLICATION: Points C, D, and E represent three apple trees in a garden. Where would you place a sprinkler so that the trees are equidistant from the sprinkler? Label the sprinkler clearly.
– Azean Khamis, Mark Humphries

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