NCERT Book Class 9 Maths Chapter 9 Circles

116 MATHEMATICS

CHAPTER 9

CIRCLES

9.1 Angle Subtended by a Chord at a Point
You have already studied about circles and its parts in Class VI.
Take a line segment PQ and a point R not on the line containing PQ. Join PR and QR
(see Fig. 9.1). Then ∠ PRQ is called the angle subtended by the line segment PQ at
the point R. What are angles POQ, PRQ and PSQ called 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.

Fig. 9.1 Fig. 9.2

Let us examine the relationship between the size of the chord and the angle
subtended by it at the centre. You may see by drawing different chords of a circle
and angles subtended by them at the centre that the longer is the chord, the bigger
will be the angle subtended by it at the centre. What will happen if you take two
equal chords of a circle? Will the angles subtended at the centre be the same
or not?