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.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 10
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.
☛ Related Questions:
- Fill in the blanks:(i) The center of the circle lies in____of the circle. (exterior / interior)(ii) A point, whose distance from the center of circle is greater than its radius lies in____of the circle. (exterior / interior)(iii) The longest chord of the 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 andof the circle.(vi) A circle divides the plane, on which it lies, inparts.
- Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centers.
- Prove that if chords of congruent circles subtend equal angles at their centers, then the chords are equal.