MA27-02 Maths Coming soon
Circle theorem: angle at the centre
MA27-02
This lesson is coming soon.
In this lesson
Prove and use the circle theorem that the angle subtended at the centre is twice the angle subtended at the circumference by the same arc, including telling the reflex and non-reflex centre angle apart.
What it covers
- Stating and briefly proving angle at the centre = 2 x angle at the circumference (same arc)
- Identifying which angle pairs genuinely share the same arc before applying the theorem
- Using the theorem chained with a basic angle fact to find an unknown angle
- The exact accepted reason wording ('the angle at the centre is twice the angle at the circumference')
Key words
For: OCR GCSE J560, Edexcel IGCSE 4MA1, AQA GCSE 8300, Edexcel GCSE 1MA1, Eduqas GCSE C300, Cambridge IGCSE 0580
On the specification
| Board | Spec | Statement |
|---|---|---|
| OCR GCSE J560 | 8.05b | Apply and prove: the angle subtended by an arc at the centre is twice the angle at the circumference. |
| Edexcel IGCSE 4MA1 | H4.6C | Understand and use angle properties of the circle including: (i) angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the remaining part of the circumference (ii) angle subtended at the circumference by a diameter is a right angle (iii) angles in the same segment are equal (iv) the sum of the opposite angles of a cyclic quadrilateral is 180° (v) the alternate segment theorem |
| AQA GCSE 8300 | G10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results |
| Edexcel GCSE 1MA1 | G10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results |
| Eduqas GCSE C300 | HG10 | Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results |
| Cambridge IGCSE 0580 | E4.7 | Circle theorems I |
For teachers
This GCSE Maths lesson teaches circle theorem: angle at the centre. By the end, students should be able to prove and use the circle theorem that the angle subtended at the centre is twice the angle subtended at the circumference by the same arc, including telling the reflex and non-reflex centre angle apart. It works through two worked examples and the mistakes examiners report.