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Questions and Answers
What is the angle subtended by the line segment PQ at the point R called?
What is the angle subtended by the line segment PQ at the point R called?
- ∠PRQ (correct)
- ∠POQ
- ∠PSQ
- ∠POR
What are ∠POQ, ∠PRQ, and ∠PSQ called in the context of Fig. 9.2?
What are ∠POQ, ∠PRQ, and ∠PSQ called in the context of 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.
- ∠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. (correct)
- ∠POQ is the angle subtended by the chord PQ at the point O, ∠PRQ and ∠PSQ are respectively the angles subtended by PQ at points R and S.
- ∠POQ is the angle subtended by the chord PQ at the point O, ∠PRQ and ∠PSQ are respectively the angles subtended by PQ at points R and S on the major and minor arcs PQ.
What happens when two equal chords of a circle are taken?
What happens when two equal chords of a circle are taken?
- The angles subtended at the centre will be different
- The angles subtended at the centre will be proportional to the length of the chords
- The angles subtended at the centre will be the same (correct)
- The angles subtended at the centre will be inversely proportional to the length of the chords
What does Theorem 9.1 state?
What does Theorem 9.1 state?
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What is to be proven in Theorem 9.1?
What is to be proven in Theorem 9.1?
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Study Notes
Angle Subtended by Line Segment
- The angle subtended by the line segment PQ at point R is known as ∠PRQ.
Angle Notation
- ∠POQ refers to the angle formed by lines OP and OQ, where O is the center of the circle.
- ∠PRQ denotes the angle at point R, created by lines PR and RQ.
- ∠PSQ is the angle formed at point S by lines PS and SQ.
Equal Chords in a Circle
- When two equal chords of a circle are taken, they subtend equal angles at the center of the circle.
- The equal chords are equidistant from the center of the circle, reinforcing the symmetric properties of the circle.
Theorem 9.1 Overview
- Theorem 9.1 states that equal chords of a circle are equidistant from the center of the circle.
- This theorem establishes a direct relationship between the lengths of chords and their positions relative to the center.
Purpose of Theorem 9.1
- The theorem aims to prove that if two chords are equal, the distances from the circle’s center to each chord are identical.
- This reinforces fundamental concepts of circle geometry and the properties of chords within circles.
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Description
Test your knowledge of angles and chords in circles with this quiz on Chapter 9 of Mathematics. Explore the concepts of angles POQ, PRQ, and PSQ and their relationship to line segments and points in a circle.
