Go to content
circle theoremAB 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

Software/Applets used on this page

JSXGraph
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.

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.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AQA AS Maths 2017Pure MathsStraight Lines and CirclesCircle Theorems
AQA AS/A2 Maths 2017Pure MathsStraight Lines and CirclesCircle Theorems
AQA GCSE (9-1) Higher (UK)G: Properties and ConstructionsG10: Circle TheoremsCircle Theorems
CBSE IX (India)GeometryCirclesTheorems
CBSE X (India)GeometryCirclesLengths of tangents from external point are equal
CIE IGCSE (9-1) Maths (0626 UK)3 GeometryB3.7 Calculating Unknown AnglesCircle Theorems
Edexcel AS Maths 2017Pure MathsCirclesCircle Theorems
Edexcel AS/A2 Maths 2017Pure MathsCirclesCircle Theorems
Edexcel GCSE (9-1) Higher (UK)G: Properties and ConstructionsG10: Circle TheoremsCircle Theorems
GCSE Higher (UK)GeometryCirclesTheorems
OCR AS Maths 2017Pure MathsLines and CirclesCircle Theorems
OCR GCSE (9-1) Higher (UK)8: Basic Geometry8.05: Circle TheoremsCircle Theorems
OCR MEI AS Maths 2017Pure MathsLines and CirclesCircle Theorems
Universal (all site questions)CCirclesTheorems