NCERT Solutions Class 9 Maths
Chapter – 10 (Circles)
The NCERT Solutions in English Language for Class 9 Mathematics Chapter – 10 Circles Exercise 10.1 has been provided here to help the students in solving the questions from this exercise.
Chapter 10: Circles
- NCERT Solution Class 9 Maths Ex – 10.2
- NCERT Solution Class 9 Maths Ex – 10.3
- NCERT Solution Class 9 Maths Ex – 10.4
- NCERT Solution Class 9 Maths Ex – 10.5
- NCERT Solution Class 9 Maths Ex – 10.6
Exercise – 10.1
1. 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.
Answer –
(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 semicircle 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.
2. Write True or False. Give reasons for your solutions.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only a 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 the diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.
Answer –
(i) Line segment joining the centre to any point on the circle is a radius of the circle. (True)
Any line segment drawn from the centre of the circle to any point on it is the radius of the circle and will be of equal length.
(ii) A circle has only a finite number of equal chords. (False)
There can be infinite numbers of equal chords in a circle.
(iii) If a circle is divided into three equal arcs, each is a major arc. (False)
For unequal arcs, there can be major and minor arcs. So, equal arcs on a circle cannot be said to be major arcs or minor arcs.
(iv) A chord of a circle, which is twice as long as its radius, is the diameter of the circle. (True)
Any chord whose length is twice as long as the radius of the circle always passes through the centre of the circle, and thus, it is known as the diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc. (False)
The region between an arc and the two radii, joining the center to the endpoints of the arc is called a sector.
(vi) A circle is a plane figure. (True)
A circle is a 2-dimensional figure. So, circle is a plane figure.
