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.
In this lesson you will use the property that tangents from an external point are equal in length (Core), and (at Extended) that equal chords are equidistant from the centre and the perpendicular bisector of a chord passes through the centre.
Objectives
- Use the symmetry property of circles that tangents from an external point are equal in length.
- Use the following symmetry properties of circles: equal chords are equidistant from the centre the perpendicular bisector of a chord passes through the centre tangents from an external point are equal in length. (Extended only)
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Lesson Note
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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 one tangent PA = 7 cm 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. a tangent point B. the midpoint only 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
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