Circles Properties and Angle Properties of Circles

Lew W. S., Sep 10, 2014

This book contains interactive activities demonstrating circle properties and angle properties based on measurement of angles and lengths. Rigorous formal proof are not included here.

Table of Contents

  1. Symmetric Properties of Circles
    1. Perpendicular Bisector of Chord (Circle Properties)
    2. Radius of Circle and Mid point of Chord (Circle Properties)
    3. Equal chords, equidistant from centre
  2. Angle Properties Circles
    1. Angles in the Same Segment
    2. Angle at Centre of Circle
    3. Angles in the SemiCircle
    4. Angles in Opposite Segments
    5. Alternate Segment Theorem
  3. Tangent to Circles Theorems
    1. Angle between line AB and radius of the circle (Tangent Radius)
    2. External Tangents to a Circle
  4. Example of Proofs involving Circle Properties
    1. Basic Proofs In Plane Geometry -Example 6 (Scaffolded)
  5. Other similar resources on Circle Properties
    1. Circle theorems
    2. Tangent-radius
    3. Angle between line AB and radius of circle (5 Jul Update)
  6. Area of Circle (Visual proof)
    1. Area of Circles

1.

Symmetric Properties of Circles

  • 1. Perpendicular Bisector of Chord (Circle Properties)
  • 2. Radius of Circle and Mid point of Chord (Circle Properties)
  • 3. Equal chords, equidistant from centre

1.1.

Perpendicular Bisector of Chord (Circle Properties)

Use the play, pause, step by step forward or backward buttons at the bottom of this applet to go through this activity.[br]Updated version at [url=https://www.geogebra.org/material/show/id/rSsUe7YM]https://www.geogebra.org/material/show/id/rSsUe7YM[/url]
Use the play, pause, step by step forward or backward buttons at the bottom of this applet to go through this activity.[br][br]At the end of this activity, what is the conclusion that you can make about this question :[br]"Perpendicular bisector of any chord on a circle will always pass through which point on this circle?"
– Lew W. S.

1.2.

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1.3.

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2.

Angle Properties Circles

  • 1. Angles in the Same Segment
  • 2. Angle at Centre of Circle
  • 3. Angles in the SemiCircle
  • 4. Angles in Opposite Segments
  • 5. Alternate Segment Theorem

2.1.

Angles in the Same Segment

This applet demonstrates the theorem of angles in the same segment.[br]You can use the slider to vary angle BCA, or drag points B, C, or D [br]and observe that angle BCA is always = angle BDA
Angles in the Same Segment
– Lew W. S.

2.2.

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2.3.

–

2.4.

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2.5.

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3.

Tangent to Circles Theorems

  • 1. Angle between line AB and radius of the circle (Tangent Radius)
  • 2. External Tangents to a Circle

3.1.

Angle between line AB and radius of the circle (Tangent Radius)

– Lew W. S.

3.2.

–

4.

Example of Proofs involving Circle Properties

  • 1. Basic Proofs In Plane Geometry -Example 6 (Scaffolded)

4.1.

Basic Proofs In Plane Geometry -Example 6 (Scaffolded)

Use this activity to aid your learning of basic proofs in plane geometry (up to and including angle properties of polygons and circles) [br]Submit your proofs with step by step justifications on pen and paper to your instructor.
– Lew W. S.

5.

Other similar resources on Circle Properties

  • 1. Circle theorems
  • 2. Tangent-radius
  • 3. Angle between line AB and radius of circle (5 Jul Update)

5.1.

Circle theorems

Demonstration of circle theorems
– Catherine Berry

5.2.

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5.3.

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6.

Area of Circle (Visual proof)

  • 1. Area of Circles

6.1.

Area of Circles

What is the area of a circle? Explore with the following applet.
Anthony Or, GeoGebra Institute of Hong Kong.
– Anthony OR 柯志明

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