# 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.

**Solution:**

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

Solution: True

Reasoning: The collection of all points in a plane, which are at a fixed distance from a fixed point in the plane is called a circle. The fixed point is the center of the circle. Fixed distance is the radius of the circle.

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

Solution: False

Reasoning: There are infinite points on the circle and hence infinite chords can be drawn between these points.

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

Solution: False

Reasoning: If PQ is a minor arc, then QRP is a major arc and it should be greater than a semicircular arc. If there are three arcs none of it can be a major arc.

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

Solution: True

Reasoning: Draw a chord that passes through the center of the circle. We can see that this chord is twice the length of the radius of the circle. This is called the diameter of the circle.

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

Solution: False

Reasoning: 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.

Solution: True

Reasoning: A circle is a 2-dimensional figure. So, circle is a plane figure.

**Video Solution:**

## 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.

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.1 Question 2:

**Summary:**

The statements (i), (iv), and (vi) are true and the statements (ii), (iii), and (v) are false.