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Paper 3
Circle Theorems
Higher
Memorise the main angle theorems.
Key Facts
- Opposite angles in a cyclic quadrilateral sum to 180°.
- Centre angle is twice the circumference angle.
Topics Covered
Angle Theorems
What you need to know
- •Angle in a semicircle is 90°.
- •Same segment angles are equal.
Exam Tips
- Quote the theorem before writing the angle value.
Cyclic Quadrilaterals
What you need to know
- •Opposite angles sum to 180°.
- •Exterior angle equals opposite interior angle.
Exam Tips
- Mark the arcs and angles clearly.
Key Terms
Cyclic quadrilateral
A quadrilateral whose vertices lie on a circle.
Tangent
A line that touches a circle at one point.
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Common Exam Questions
Angle at centre is 110°. Angle at circumference?
2 markseasyPaper 3
Model Answer
55°
What examiners want to see
- ✓Centre angle is twice circumference angle.
Angles in the same segment are?
1 markeasyPaper 3
Model Answer
Equal
What examiners want to see
- ✓State the theorem.
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