IGCSEMathsEdexcelMaths AHigherRevision NotesGeometry & TrigonometryCircle TheoremsAngles in the Same Segment

Angles in the Same Segment (Edexcel IGCSE Maths A): Revision Note

Amber

Written by: Amber

Reviewed by: Dan Finlay

Updated on

Edexcel Maths A: HigherEdexcel Maths A (Modular): Higher Unit 2Cambridge (CIE) International Maths: ExtendedCambridge (CIE) Maths: Extended

Did this video help you?

Circles & Segments

Circle Theorem: Angles in the same segment are equal

  • Any two angles on the circumference of a circle that are formed from the same two points on the circumference are equal

    • These two angles are in the same segment of the circle

      • To see this, add the chord PQ below to split the circle into two segments

A circle with points P and Q and the arc between them highlighted. Two chords from each point meet at another point on the circumference forming an angle y.

  • To spot this circle theorem on a diagram

    • Find two points on the circumference that meet at a third point

    • See if there are any other pairs of lines from the same two original points that meet at a different point on the circumference

  • When explaining this theorem in an exam you must use the keywords:

    • Angles in the same segment are equal

  • Look out for a bowtie shape

    • The theorem works upside down, in that the angles at P and Q are also equal

Angles in the same segment are equal (this works upside-down too)

Examiner Tips and Tricks

  • An exam question diagram may have multiple equal angles

    • Look for as many as possible by seeing how many pairs of lines start from the same two points on the circumference

Worked Example

The diagram below shows a circle with centre, O.
A, B, C, D and E are five points on the circumference on the circle.

Angle AEB = 12º.
Angle BEC = 14º.
Angle CED = 73º.
Angle EBD = θº.

Find the value of θ .

A circle with centre, O, and 5 points on the circumference, A, B, C, D and E. Angle AEB = 12º, angle BEC = 14º and angle CED = 73º. The angle EBC = θ º.

CE is a diameter
This means that triangles EAC and CED are both triangles in a semicircle

Angle EAC = 90º
Angle CED = 90º
Angle in a semicircle = 90º

Find the other angles in the triangles

Angle ECA = 64º
Angle ECD = 17º
Angles in a triangle = 180º

Label these angles on the diagram

Previous circle diagram with the angle EAC and EDC marked as right angles. Angle ACE = 64º and angle DCE = 17º are also labelled.

Angle θ  is formed by two lines coming from either end of the chord ED
Angle ECD is also formed by two lines coming from either end of the chord ED

Angle θ = angle ECD = 17º
Angles in the same segment are equal

Angle θ = 17º

👀 You've read 1 of your 5 free revision notes this week
An illustration of students holding their exam resultsUnlock more revision notes. It's free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Test yourselfFlashcards

Did this page help you?

Previous:Angles in Cyclic QuadrilateralsNext:The Alternate Segment Theorem
Author
Reviewer
Amber

Author: Amber

Expertise: Maths Content Creator

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Download notes on Angles in the Same Segment