Circle Theorems
Overview
Circle theorems are a set of elegant rules about the angles and lines inside a circle. They look like magic at first, but each one is reliable and, used together, they let you find angles that would otherwise be impossible to reach.
In this lesson you will calculate angles using circle properties: the angle in a semicircle and the tangent-radius right angle at Core, plus (at Extended) the angle at the centre, angles in the same segment, cyclic quadrilaterals and the alternate segment theorem.
Objectives
- Calculate unknown angles and give explanations using the following geometrical properties of circles: angle in a semicircle = 90° angle between tangent and radius = 90°.
- Calculate unknown angles and give explanations using the following geometrical properties of circles: angle in a semicircle = 90° angle between tangent and radius = 90° angle at the centre is twice the angle at the circumference angles in the same segment are equal opposite angles of a cyclic quadrilateral sum to 180° (supplementary) alternate segment theorem. (Extended only)
Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Circle Theorems. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- The angle in a semicircle is: A. 45° B. 60° C. 90° D. 180° Answer: C
- The angle between a tangent and a radius is: A. 0° B. 45° C. 90° D. 180° Answer: C
- An angle at the centre is 100°. The angle at the circumference on the same arc is: A. 50° B. 100° C. 180° D. 200° Answer: A
- Opposite angles of a cyclic quadrilateral add up to: A. 90° B. 180° C. 270° D. 360° Answer: B
- One angle of a cyclic quadrilateral is 85°. Its opposite angle is: A. 85° B. 95° C. 105° D. 275° Answer: B
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Recommended Books
Practice Mock Questions
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