Circle theorems: GCSE Maths revision
Circle theorems are named angle facts. State the theorem as your reason. Sketch and mark equal angles before you calculate.
Theorems to learn
- Angle in a semicircle is 90°
- Angle at the centre is twice the angle at the circumference
- Angles in the same segment are equal
- Opposite angles in a cyclic quadrilateral sum to 180°
- A tangent is perpendicular to the radius at the point of contact
- Tangents from a common point are equal
- Alternate segment theorem
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
A triangle is inscribed in a semicircle with the diameter as one side. What is the angle at the top?
Angle at the circumference is 34°. Angle at the centre standing on the same arc?
One angle of a cyclic quadrilateral is 110°. The opposite angle?
Common mistakes
- Using a theorem that does not apply (the points must be on the circle).
- Forgetting to write the theorem name.
Answers and working
Frequently asked questions
Are circle theorems on Foundation?
They are Higher-tier content on GCSE Maths.
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