Geometrical Properties in a Circle

ctc, 27 Oct 2014

Table of Contents

  1. Definitions
    1. Parts of a Circle
    2. Types of angles and arcs
  2. Property 1
    1. Angles at centre and circumference
  3. Property 2
    1. Angles in a semi-circle
  4. Property 3
    1. Angles in the same segment
  5. Cyclic Quadrilaterals
    1. Opposite angles in Cyclic Quad
    2. Exterior angles of a Cyclic Quadrilateral
  6. Tangents to the circle
    1. Secants vs Tangents
    2. Tangent and Radius
    3. Alternate Segment theorem (Tangent-Chord theorem)
    4. Two Tangents from an External Point
  7. Symmetrical Properties
    1. Line of symmetry for a triangle
    2. Symmetrical Property 1
    3. Symmetrical Property 2

1.

Definitions

  • 1. Parts of a Circle
  • 2. Types of angles and arcs

1.1.

Parts of a Circle

Please wait for the applet to load. It may take several seconds.[br]Drag points A or B.[br]To see the part(s) of a circle, click on the check box(es).[br]To refresh the screen, click on the refresh icon on the top-right-hand corner of the applet.
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1.2.

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2.

Property 1

Angles at centre and circumference

  • 1. Angles at centre and circumference

2.1.

Angles at centre and circumference

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3.

Property 2

Angle in semi-circle

  • 1. Angles in a semi-circle

3.1.

Angles in a semi-circle

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4.

Property 3

Angles in the same segment

  • 1. Angles in the same segment

4.1.

Angles in the same segment

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5.

Cyclic Quadrilaterals

  • 1. Opposite angles in Cyclic Quad
  • 2. Exterior angles of a Cyclic Quadrilateral

5.1.

Opposite angles in Cyclic Quad

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5.2.

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6.

Tangents to the circle

  • 1. Secants vs Tangents
  • 2. Tangent and Radius
  • 3. Alternate Segment theorem (Tangent-Chord theorem)
  • 4. Two Tangents from an External Point

6.1.

Secants vs Tangents

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6.2.

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6.3.

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6.4.

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7.

Symmetrical Properties

  • 1. Line of symmetry for a triangle
  • 2. Symmetrical Property 1
  • 3. Symmetrical Property 2

7.1.

Line of symmetry for a triangle

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7.2.

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7.3.

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Information