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Questions and Answers
What is the angle subtended by the line segment PQ at the point R called?
The angle subtended by the line segment PQ at the point R is called ∠PRQ.
What are angles POQ, PRQ and PSQ called in Fig. 9.2?
In Fig. 9.2, ∠POQ is the angle subtended by the chord PQ at the centre O, ∠PRQ and ∠PSQ are respectively the angles subtended by PQ at points R and S on the major and minor arcs PQ.
What is the relationship between the size of the chord and the angle subtended by it at the centre?
The relationship is that the longer the chord, the bigger the angle subtended by it at the centre.
What is the significance of examining the relationship between the size of the chord and the angle subtended by it at the centre?
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What happens if you take two equal chords of a circle?
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Study Notes
Angle Subtended by a Line Segment
- The angle subtended by the line segment PQ at the point R is called the angle subtended by the chord PQ at the centre R.
Types of Angles
- Angles POQ, PRQ, and PSQ are called angles subtended by the chord at the centre.
Relationship between Chord Size and Angle
- The size of the chord and the angle subtended by it at the centre are directly proportional.
- A larger chord subtends a larger angle at the centre, and a smaller chord subtends a smaller angle at the centre.
Significance of Examining the Relationship
- Examining the relationship between the size of the chord and the angle subtended by it at the centre helps in understanding the properties of circles and their applications.
Equal Chords
- If you take two equal chords of a circle, they will subtend equal angles at the centre.
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Description
Test your knowledge of circle geometry with this quiz on angles subtended by chords at points. Identify angles like POQ, PRQ, and PSQ as you explore the properties of circles in mathematics.
