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 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.
Answer it.
Answers
Answer:
Vi A circle is a plane figure are the ture
Solution:-
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
Answer:- True
Reason:- Because, 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.
Answer:- False
Reason:- A circle has infinity number of chords but every chords are not equal.
Correct statement:- A circle has infinity number of chords but every chords are not equal.
(iii) If a circle is divided into three equal arcs, each is a major arc.
Answer:- False
Reason:- It is false because a major Arc is always bigger than a minor arc so they cannot be equal.
Correct statement:- If a circle is divided into three equal arcs each will not be a major arc.
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
Answer:- True
Reason:- Because a diameter is the longest chord of a circle and Diameter = 2 × radius
(v) Sector is the region between the chord and its corresponding arc.
Answer:- False
Reason:- The region between the chord and its corresponding Arc is called segment
Correct statement:- Segment is the region between the chords and its corresponding arc.
(vi) A circle is a plane figure.
Answer:- True
Reason:- A circle is a plane figure with no line segment.
Remember:-
- Diameter is the longest chord of a circle.
- Radius = Diameter / 2
- All radii are equal.
- The perimeter of a circle is also called circumference.