MA27-03 Maths Coming soon
Circle theorem: angle in a semicircle
MA27-03
This lesson is coming soon.
In this lesson
Prove and use the circle theorem that the angle subtended at the circumference by the diameter (angle in a semicircle) is 90 degrees, using the exact accepted reason wording.
What it covers
- The angle in a semicircle (subtended by the diameter) is 90 degrees
- Spotting a diameter as the trigger for this fact, in any orientation
- The exact accepted reason wording ('angle in a semicircle is 90 degrees')
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 | 8.05c | Apply and prove: the angle on the circumference subtended by a diameter is a right angle. |
| 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 | C4.7 | Circle theorems |
| Cambridge IGCSE 0580 | E4.7 | Circle theorems I |
For teachers
This GCSE Maths lesson teaches circle theorem: angle in a semicircle. By the end, students should be able to prove and use the circle theorem that the angle subtended at the circumference by the diameter (angle in a semicircle) is 90 degrees, using the exact accepted reason wording. It works through two worked examples and the mistakes examiners report.