Class 9, NCERT (CBSE) Mathematics | Chapter 10, CIRCLES

Class IX, Mathematics (Circles)

NCERT (CBSE) Textbook Exercise 10.1 Solution

(Page 171)

Q1: Fill in the blanks

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

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

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

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

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

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

Ans 1:

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

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

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

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

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

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

Q2: Write True or False. Give reasons for your answers.

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

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

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

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

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

(vi) A circle is a plane figure.

Ans 2:

(i) True. All the points on the circle are at equal distances from the centre of the circle, and this distance is called as radius of the circle.

(ii) False. There are infinite points on a circle and we can draw infinite number of chords of given length. Hence, a circle has infinite number of equal chords.

(iii) False. Because of each arc, the remaining arc will have greater length.  

(iv) True. Twice the length of radius of any circle is its diameter.

(v) False by virtue of its definition.

(vi) True. A circle is always two-dimensional figure which is also a part of a plane.