Geometry of Circles

Hlho, 12 apr. 2019

Book 4B Chapter 11-12

Inhoudstafel

  1. Chapter 11 Basic Properties of Circles
    1. Theorem 1: Perpendicular from centre to chord bisects chord
    2. Theorem 2: Line Joining Centre to Mid-pt. of Chord Perp. to Chord
    3. Theorem 3: Perp. Bisector of Chord passes through Centre
    4. Theorem 4 Equal Chords, Equidistant from Centre
    5. Theorem 5: Chords Equidistant from Centre are Equal
    6. Theorem 5 Chords equidistant from centre are equal
    7. Theorem 6 Angle at Centre Twice Angle at Circumference
    8. Proof of Theorem 6: Angle at Centre Twice Angle at Circumference
    9. Theorem 7: Angle in Semi-circle
    10. Theorem 9: Angles in the same segment
    11. Theorem 10-12: Relationships among Chords, Arcs and Angles
    12. Theorem 13: Arcs prop to angle at centre
    13. Theorem 14 Arcs prop to angles at circumference
  2. Chapter 12 More about Basic Properties of Circles
    1. Theorem 1 Opp Angles, Cyclic Quad
    2. Theorem 2: Ext. angle, cyclic quad
    3. Tests for Cyclic Quadrilaterals (1)
    4. Tests for Cyclic Quadrilaterals (2)
    5. Theorem 6: Tangent perpendicular to Radius
    6. Theorem 8 Tangent Properties
    7. Theorem 9 Angles in alternate segment

1.

Chapter 11 Basic Properties of Circles

  • 1. Theorem 1: Perpendicular from centre to chord bisects chord
  • 2. Theorem 2: Line Joining Centre to Mid-pt. of Chord Perp. to Chord
  • 3. Theorem 3: Perp. Bisector of Chord passes through Centre
  • 4. Theorem 4 Equal Chords, Equidistant from Centre
  • 5. Theorem 5: Chords Equidistant from Centre are Equal
  • 6. Theorem 5 Chords equidistant from centre are equal
  • 7. Theorem 6 Angle at Centre Twice Angle at Circumference
  • 8. Proof of Theorem 6: Angle at Centre Twice Angle at Circumference
  • 9. Theorem 7: Angle in Semi-circle
  • 10. Theorem 9: Angles in the same segment
  • 11. Theorem 10-12: Relationships among Chords, Arcs and Angles
  • 12. Theorem 13: Arcs prop to angle at centre
  • 13. Theorem 14 Arcs prop to angles at circumference

1.1.

Theorem 1: Perpendicular from centre to chord bisects chord

– Hlho, Lambda Math

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

1.13.

–

2.

Chapter 12 More about Basic Properties of Circles

  • 1. Theorem 1 Opp Angles, Cyclic Quad
  • 2. Theorem 2: Ext. angle, cyclic quad
  • 3. Tests for Cyclic Quadrilaterals (1)
  • 4. Tests for Cyclic Quadrilaterals (2)
  • 5. Theorem 6: Tangent perpendicular to Radius
  • 6. Theorem 8 Tangent Properties
  • 7. Theorem 9 Angles in alternate segment

2.1.

Theorem 1 Opp Angles, Cyclic Quad

Instructions
Drag any point in the figure and observe the sum of opposite angles of a cyclic quadrilateral.
– Hlho

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

Informatie