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Angles and Chords in Circles

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Questions and Answers

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?

∠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?

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?

<p>Equal chords of a circle subtend equal angles at the centre</p> Signup and view all the answers

What is to be proven in Theorem 9.1?

<p>∠AOB = ∠COD</p> Signup and view all the answers

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.