Basic Properties of Circles

Anthony OR 柯志明, Dec 17, 2024

Table of Contents

  1. Distances between Chords and Centre
    1. Equal Chords
    2. Chords Equidistant from Centre
  2. Angles in a Circle
    1. Angles at the Centre and Angles at the Circumference
    2. Angle in Semi-circle
    3. Converse of Angle in Semi-circle
    4. Angles in the Same Segment
  3. Relationships among Arcs, Chords and Angles
    1. Explore Relationships among Angles, Arcs and Chords of Circles
    2. Relationship between Angles at the Circumference and Arcs
  4. Cyclic Quadrilaterals
    1. Opposite Angles of a Cyclic Quadrilateral
    2. Exterior Angle of a Cyclic Quadrilateral
  5. Concyclic Points
    1. Converse of Angles in the Same Segment
    2. Opposite Angles Supplementary
    3. Exterior Angle Equals Interior Opposite Angle

1.

Distances between Chords and Centre

  • 1. Equal Chords
  • 2. Chords Equidistant from Centre

1.1.

Equal Chords

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1.2.

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2.

Angles in a Circle

  • 1. Angles at the Centre and Angles at the Circumference
  • 2. Angle in Semi-circle
  • 3. Converse of Angle in Semi-circle
  • 4. Angles in the Same Segment

2.1.

Angles at the Centre and Angles at the Circumference

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2.2.

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2.3.

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2.4.

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3.

Relationships among Arcs, Chords and Angles

  • 1. Explore Relationships among Angles, Arcs and Chords of Circles
  • 2. Relationship between Angles at the Circumference and Arcs

3.1.

Explore Relationships among Angles, Arcs and Chords of Circles

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3.2.

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4.

Cyclic Quadrilaterals

  • 1. Opposite Angles of a Cyclic Quadrilateral
  • 2. Exterior Angle of a Cyclic Quadrilateral

4.1.

Opposite Angles of a Cyclic Quadrilateral

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4.2.

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5.

Concyclic Points

  • 1. Converse of Angles in the Same Segment
  • 2. Opposite Angles Supplementary
  • 3. Exterior Angle Equals Interior Opposite Angle

5.1.

Converse of Angles in the Same Segment

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5.2.

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5.3.

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