AB is a chord of the circle. C and D are points on the circumference. Use your mouse to change the size of the circle,or the positions of the centre, points A, B, C or D. Observe the angles at C and D.

However you alter the diagram, the angles at C and D will remain identical to each other. Thus...

The angles in the same segment are equal

However you alter the diagram, the angles at C and D will remain identical to each other. Thus...

The angles in the same segment are equal

## Software/Applets used on this page

This page uses JSXGraph

JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.

JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.

## Glossary

### chord

A straight line joining two points on a circle or other curve.

### circle

a conic curve with equation (x-a)²+(y-b)²=r²

### function

A rule that connects one value in one set with one and only one value in another set.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

GCSE Higher (UK) | Geometry | Circles | Theorems | - |

Universal (all site questions) | C | Circles | Theorems | - |

CBSE X (India) | Geometry | Circles | Lengths of tangents from external point are equal | - |

CBSE IX (India) | Geometry | Circles | Theorems | - |

Edexcel GCSE (9-1) Higher (UK) | G: Properties and Constructions | G10: Circle Theorems | Circle Theorems | - |

OCR GCSE (9-1) Higher (UK) | 8: Basic Geometry | 8.05: Circle Theorems | Circle Theorems | - |

AQA GCSE (9-1) Higher (UK) | G: Properties and Constructions | G10: Circle Theorems | Circle Theorems | - |

CIE IGCSE (9-1) Maths (0626 UK) | 3 Geometry | B3.7 Calculating Unknown Angles | Circle Theorems | - |

Edexcel AS/A2 Maths 2017 | Pure Maths | Circles | Circle Theorems | - |

Edexcel AS Maths 2017 | Pure Maths | Circles | Circle Theorems | - |

AQA AS Maths 2017 | Pure Maths | Straight Lines and Circles | Circle Theorems | - |

OCR AS Maths 2017 | Pure Maths | Lines and Circles | Circle Theorems | - |

OCR MEI AS Maths 2017 | Pure Maths | Lines and Circles | Circle Theorems | - |

AQA AS/A2 Maths 2017 | Pure Maths | Straight Lines and Circles | Circle Theorems | - |