Symmetrical Properties of Circles

Norhuda Mohd Sadekan, Jul 29, 2015

The basic interactive materials serve 2 purposes in teaching and learning of properties of chords of circles: 1. Enable teachers to use it to illustrate the properties of chords of circles, 2. Enable students to use it for exploratory purposes.

Table of Contents

  1. Properties of Chords of Circles
    1. Perpendicular Bisector of Chord
    2. Perpendicular from centre to chord bisects chord
    3. Equal chords are equidistant from the centre of the circle
  2. Tangents to a circle
    1. Converse of Tangent perpendicular to radius
    2. Two tangents to a circle
    3. Tangents from the external points are equal in length
  3. Angle Properties of Circles
  4. Cyclic Quadrilaterals
  5. Alternate Segment Theorem

1.

Properties of Chords of Circles

  • 1. Perpendicular Bisector of Chord
  • 2. Perpendicular from centre to chord bisects chord
  • 3. Equal chords are equidistant from the centre of the circle

1.1.

Perpendicular Bisector of Chord

[b]Sliders for changing the following:[/b][br]1. Radius of the circle,[br][br][b]Blue dots for changing the lengths of the chords:[/b][br]1. BC.[br][br][b]Pre-requisite knowledge and terms:[/b] Perpendicular bisector, Chord[br][br][b]Task:[/b] Explore and manipulate the applet. Make a conjecture on the property of the chord and record it in your class wall. [br][br][b]Questions to guide in Investigation 1: [/b][br][br]1a) For the various lengths of the chord BC, what can you say about the lengths of BD and DC? Why do they behave so? [br][br]1b) Where is the centre of the circle located? Is it true for various lengths of BC?[br][br]1c) What is your conjecture of the property of the chord here? Write it on your class wall.
Perpendicular Bisector of Chord
– Norhuda Mohd Sadekan

1.2.

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1.3.

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2.

Tangents to a circle

  • 1. Converse of Tangent perpendicular to radius
  • 2. Two tangents to a circle
  • 3. Tangents from the external points are equal in length

2.1.

Converse of Tangent perpendicular to radius

Converse of Tangent perpendicular to radius
Converse of Tangent perpendicular to radius
– mcdull

2.2.

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2.3.

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3.

Angle Properties of Circles


    This chapter does not contain any resources yet.

4.

Cyclic Quadrilaterals


    This chapter does not contain any resources yet.

5.

Alternate Segment Theorem


    This chapter does not contain any resources yet.

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