Green Bridge Learning Resource For Circle Theorems II

Overview

Beyond the angle theorems, circles have neat symmetry properties about their chords and tangents. These let you find lengths and prove that certain lines pass through the centre, and they round out your toolkit for circle problems.

In this lesson (Extended tier) you will use three symmetry properties of circles: equal chords are equidistant from the centre, the perpendicular bisector of a chord passes through the centre, and tangents from an external point are equal in length.

Lesson Evaluation

Congratulations on completing the lesson on Circle Theorems II. 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.

Two tangents from an external point P are: A. perpendicular B. equal in length C. parallel D. always 90° Answer: B
If PA = 7 cm is one tangent from P, the other tangent PB is: A. 3.5 cm B. 7 cm C. 14 cm D. cannot tell Answer: B
The perpendicular from the centre to a chord: A. bisects the chord B. is a tangent C. equals the radius D. is a diameter Answer: A
The perpendicular bisector of a chord passes through: A. the midpoint only B. a tangent point C. the centre D. an external point Answer: C
Equal chords in a circle are: A. parallel B. perpendicular C. equidistant from the centre D. diameters Answer: C