Moving Circle Theorems

Ben Sparks, Mar 19, 2021

8 Circle Theorems discussed at GCSE level (UK) Animated The statements of the theorems are not perfectly rigorous (this is intentional). The proofs are not stated formally, and should form the basis of class discussion, leading to more formal proofs if required.

Table of Contents

  1. Circle Theorems
    1. 8 Circle Theorems
    2. Angle at the centre
    3. Angles in the same segment
    4. Angle in a semicircle
    5. Opposite angles in cyclic quadrilaterals
    6. Tangent meets a radius
    7. Tangents from a point
    8. Bisector of a chord
    9. Angles in the alternate segment
  2. Circle Theorem Visual Proofs
    1. Angle at the centre proof
    2. Angles in the same segment proof
    3. Angle in a semicircle proof
    4. Opposite angles in Cyclic Quadrilateral proof
    5. Tangent and radius proof
    6. Tangents from a point proof
    7. Chord bisector proof
    8. Alternate Segment Proof Hints

1.

Circle Theorems

  • 1. 8 Circle Theorems
  • 2. Angle at the centre
  • 3. Angles in the same segment
  • 4. Angle in a semicircle
  • 5. Opposite angles in cyclic quadrilaterals
  • 6. Tangent meets a radius
  • 7. Tangents from a point
  • 8. Bisector of a chord
  • 9. Angles in the alternate segment

1.1.

8 Circle Theorems

Zoom in (mouse wheel) to your favourite.[br][br]What's changing and what's staying the same?
– Ben Sparks

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1.7.

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1.8.

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1.9.

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2.

Circle Theorem Visual Proofs

  • 1. Angle at the centre proof
  • 2. Angles in the same segment proof
  • 3. Angle in a semicircle proof
  • 4. Opposite angles in Cyclic Quadrilateral proof
  • 5. Tangent and radius proof
  • 6. Tangents from a point proof
  • 7. Chord bisector proof
  • 8. Alternate Segment Proof Hints

2.1.

Angle at the centre proof

– Ben Sparks

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2.8.

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