Circle theorems workout

Help students master circle theorems with this comprehensive GCSE maths resource, featuring a PowerPoint presentation and practice worksheet designed to build confidence and exam skills.

What's included

• Step-by-step PowerPoint presentation with accompanying worksheet
• Progressive practice questions are integrated throughout to check understanding
• Exam-style questions with worked solutions to build exam confidence

Access the worksheet as a free PDF download, or subscribe to unlock the editable PowerPoint and worksheet versions.

What are circle theorems?

Circle theorems are fundamental geometric principles that describe the relationships between angles, lines and points within circles. There are 7 key circle theorems:

1. Angles in the same segment Angles in the same segment of a circle are equal.
2. Angle at the centre The angle at the centre is twice the angle at the circumference when both angles are subtended by the same arc.
3. Cyclic quadrilateral angles Opposite angles in a cyclic quadrilateral sum to 180 degrees.
4. Angle in a semicircle The angle in a semicircle is 90 degrees (a right angle).
5. Perpendicular from centre A perpendicular line from the centre of a circle to a chord bisects the chord.
6. Radius and tangent The radius of a circle is perpendicular to the tangent at the point of contact.
7. Alternate segment theorem The angle between a tangent and a chord at the point of contact equals the angle in the alternate segment.

This circle theorems resource covers:

• circle facts
• the meaning of subtend
• angles in the same segment
• angles at the centre of the circle and the circumference of a circle
• cyclic quadrilaterals
• angle in a semi-circle
• the alternate segment theorem

Circle theorems in GCSE maths

This resource supports the GCSE mathematics curriculum across all major exam boards (AQA, Edexcel and OCR). Students will develop skills in:

• Recognising and applying circle theorems to solve problems
• Finding angles using multiple circle theorems
• Working with cyclic quadrilaterals and isosceles triangles
• Constructing mathematical proofs using circle theorems

How to use this resource

Perfect for both classroom teaching and independent study, this resource can be used to introduce circle theorems or as a comprehensive revision tool. The PowerPoint follows a logical progression, allowing teachers to pause for discussion and worked examples, while the accompanying worksheet provides structured practice opportunities.

Looking for more like this?

Enhance your geometry teaching with these related resources:

• Parts of a circle - interactive resource
• GCSE circle theorem revision cards
• Investigating circles - student workbook

For more geometry resources, visit our complete circles and geometry collection