Geometry of Circles

Hlho, Apr 12, 2019

Book 4B Chapter 11-12

Table of Contents

  1. Chapter 11 Basic Properties of Circles
    1. Theorem 1.1 - 1.3 (Chords of circles)
    2. Theorem 1.4-1.5 Distances between Chords and Centre
    3. Theorem 1.6 Angle at Centre Twice Angle at Circumference
    4. Theorem 1.9 Angles in the same segment
    5. Theorem 1.10-1.15 Relationships among Chords, Arcs and Angles
    6. Theorem 1.18 Opp Angles, Cyclic Quad
    7. Theorem 1.19 ext. angle, cyclic quad.
    8. Theorem 1.20-1.23 Tests of Concyclic Points
  2. Chapter 12 Tangents to Circles
    1. Theorem 2.1 Tangent perpendicular to Radius
    2. Theorem 2.4 Tangent Properties
    3. Theorem 2.5 Angles in alternate segment

1.

Chapter 11 Basic Properties of Circles

  • 1. Theorem 1.1 - 1.3 (Chords of circles)
  • 2. Theorem 1.4-1.5 Distances between Chords and Centre
  • 3. Theorem 1.6 Angle at Centre Twice Angle at Circumference
  • 4. Theorem 1.9 Angles in the same segment
  • 5. Theorem 1.10-1.15 Relationships among Chords, Arcs and Angles
  • 6. Theorem 1.18 Opp Angles, Cyclic Quad
  • 7. Theorem 1.19 ext. angle, cyclic quad.
  • 8. Theorem 1.20-1.23 Tests of Concyclic Points

1.1.

Theorem 1.1 - 1.3 (Chords of circles)

Instructions
Drag the point B to observe [br]1. the relationship between BD and CD, and[br]2. the relationship between AD and BC.
Theorem 1.1 - 1.3
If AD is perpendicular to BC, BD =
Theorem 1.1 - 1.3
If BD = CD, then [math]\angle[/math]ADC =___[math]^{\circ}[/math].
– Hlho

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

Chapter 12 Tangents to Circles

  • 1. Theorem 2.1 Tangent perpendicular to Radius
  • 2. Theorem 2.4 Tangent Properties
  • 3. Theorem 2.5 Angles in alternate segment

2.1.

Theorem 2.1 Tangent perpendicular to Radius

Move the point on the circumference of the circle. What do you notice about the angle in the circle?
– Hlho, MrDoyle

2.2.

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2.3.

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