Chapter 10: Circles

EXERCISE 10.1

1. Fill in the blanks :

(i) The centre of a circle lies in                   of the circle . (Exterior/interior)

Answer : interior .

(ii) A point, whose distance from the centre of a circle is greater than its radius lies in                  of the circle . (exterior/interior)

Answer : Exterior .

(iii) The longest chord of a circle is a                 of the circle .

Answer : Diameter .

(iv) An arc is a                    when its ends are the ends of a diameter .

Answer : Semicircle .

(v) Segment of a circle is the region between an arc and                    of the circle .

Answer : The chord .

(vi) A circle divides the plane, on which it lies , in                   parts .

Answer : Three .

2. Write True or False : Given reasons for your answers .

(i) Line segment joining the centre to any point on the circle is a radius of the circle .

Answer : True .

(ii) A circle has only finite number of equal chords .

Answer : False .

(iii) If a circle is divided into three equal arcs, each is a major arc .

Answer : False .

(iv) A chord of a circle , which is twice as long as its radius, is a diameter of the circles .

Answer : True .

(v) Sector is the region between the chord and its corresponding arc .

Answer : False .

(vi) A circle is a plane figure .

Answer : True .

EXERCISE 10.2
1. Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Solution:  Given, O and O’ be the centres of the two circles and AB = CD .

To prove : ∠AOB=∠CO'D .

Proof: In ∆AOB and  ∆CO'D , we have

AB=CD  [Chord]

  OA=O'C  [Radius]

  OB=O'D [Radius]

∆AOB≅∆CO'D  [SSS]

∠AOB=∠CO'D  [CPCT]   Proved.