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Apply Circle Theorems to Solve Problems

In this worksheet, students will apply circle theorems to solve problems.

'Apply Circle Theorems to Solve Problems' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   OCR, AQA, Eduqas, Pearson Edexcel,

Curriculum topic:   Basic Geometry, Geometry and Measures

Curriculum subtopic:   Circles Properties and Constructions

Difficulty level:  

Worksheet Overview

Cavemen with a circle

What did the caveman say to his mate?

Do you want to go clubbing tonight?


We have a lot to thank the caveman for (or whoever) that invented the wheel.  

Circles are a huge part of our everyday life, from a potters wheel, jewelry, clocks, and wheels.  

Engineers owe a lot to the study of circles as gears rely on them.  Can you think of any more?


Circle theorems help to solve problems in many ways.

Lets remind ourselves of the theorems


Angles at the centre are twice that on the circumference.

Angles in the same segment are equal

Angles in the same segment


Angle subtended from the diameter is 90°

Triangle in a semi circle

Opposite angles in cyclic quadrilaterals add up to 180°

cyclic quadrilateral


Tangents to a circle meet the circumference at 90° and the lines are of equal length.

Tangents to a circle

Chords and radii

Angles in alternate segments are equal

The trick to being successful in these questions is to be able to spot the theorems. 

magic wand and top hat

In problems solving questions, there is usually more than one theorem to follow.  

Quite often you will have to find angles that are not identified first.


Lets investigate the magic.

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