RD Sharma Solutions: Circles (Exercise 14.1)

# Circles (Exercise 14.1) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download

``` Page 1

1. Explain the following:
(i) Circle
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle.
Solution:

(i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant.

(ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre.

(iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points.

(iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is
called a diameter of the circle.

(v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle.

(vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a
circle.

2. Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the same
centre O.
Solution:

The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre.

3. Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle.
Join AB, BC, CD and DA.
Solution:

Page 2

1. Explain the following:
(i) Circle
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle.
Solution:

(i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant.

(ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre.

(iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points.

(iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is
called a diameter of the circle.

(v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle.

(vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a
circle.

2. Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the same
centre O.
Solution:

The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre.

3. Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle.
Join AB, BC, CD and DA.
Solution:

The figure given below shows a circle with centre O and two perpendicular diameter AC and BD.

4. Draw a circle with centre O and radius 6 cm. Mark points P, Q, R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.
Rewrite each of the following statements using the correct symbol (=, < or >):
(i) OQ …… 5 cm  (ii) OP ……. 5 cm  (iii) OR …... 5 cm.
Solution:

The figure given below shows the points P, Q and R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.

The statements can be written as
(i) OQ < 5 cm

(ii) OP = 5 cm

(iii) OR > 5 cm
Page 3

1. Explain the following:
(i) Circle
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle.
Solution:

(i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant.

(ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre.

(iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points.

(iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is
called a diameter of the circle.

(v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle.

(vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a
circle.

2. Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the same
centre O.
Solution:

The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre.

3. Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle.
Join AB, BC, CD and DA.
Solution:

The figure given below shows a circle with centre O and two perpendicular diameter AC and BD.

4. Draw a circle with centre O and radius 6 cm. Mark points P, Q, R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.
Rewrite each of the following statements using the correct symbol (=, < or >):
(i) OQ …… 5 cm  (ii) OP ……. 5 cm  (iii) OR …... 5 cm.
Solution:

The figure given below shows the points P, Q and R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.

The statements can be written as
(i) OQ < 5 cm

(ii) OP = 5 cm

(iii) OR > 5 cm

5. Take two points A and B on the page of your note book. Draw a circle with centre A which passes
through B.
Solution:

The figure given below shows the circle with A as centre and a line which passes through B.

6. Draw a semi-circle with centre O and radius 5 cm. Is the diameter that determines the semi-circle, a part
of the semi-circle?
Solution:

The figure given below shows a semi-circle with centre O and radius 5 cm.

We know that a semi-circle is the end point of a diameter which divides the circle into two equal parts.
No, the diameter does not determine the semi-circle and it is the end points of the diameter which finds the semi-
circle or a part of the semi-circle.

7. The diameter of a circle is 14 cm, find its radius.
Solution:

It is given that
Diameter of a circle = 14 cm
We know that
Radius of a circle = Diameter / 2
By substituting the values
Page 4

1. Explain the following:
(i) Circle
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle.
Solution:

(i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant.

(ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre.

(iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points.

(iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is
called a diameter of the circle.

(v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle.

(vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a
circle.

2. Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the same
centre O.
Solution:

The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre.

3. Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle.
Join AB, BC, CD and DA.
Solution:

The figure given below shows a circle with centre O and two perpendicular diameter AC and BD.

4. Draw a circle with centre O and radius 6 cm. Mark points P, Q, R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.
Rewrite each of the following statements using the correct symbol (=, < or >):
(i) OQ …… 5 cm  (ii) OP ……. 5 cm  (iii) OR …... 5 cm.
Solution:

The figure given below shows the points P, Q and R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.

The statements can be written as
(i) OQ < 5 cm

(ii) OP = 5 cm

(iii) OR > 5 cm

5. Take two points A and B on the page of your note book. Draw a circle with centre A which passes
through B.
Solution:

The figure given below shows the circle with A as centre and a line which passes through B.

6. Draw a semi-circle with centre O and radius 5 cm. Is the diameter that determines the semi-circle, a part
of the semi-circle?
Solution:

The figure given below shows a semi-circle with centre O and radius 5 cm.

We know that a semi-circle is the end point of a diameter which divides the circle into two equal parts.
No, the diameter does not determine the semi-circle and it is the end points of the diameter which finds the semi-
circle or a part of the semi-circle.

7. The diameter of a circle is 14 cm, find its radius.
Solution:

It is given that
Diameter of a circle = 14 cm
We know that
Radius of a circle = Diameter / 2
By substituting the values

Radius of a circle = 14/2 = 7 cm.

8. Given a circle with centre O and radius 2.5 cm, what is the length of the longest chord of the circle.
Solution:

We know that the diameter of a circle is its longest chord which is twice its radius.
So the length of the longest chord of the circle = 2 (2.5) = 5 cm.

9. Fill in the blanks:
(i) The diameter of a circle is ……. times its radius.
(ii) The diameter of a circle is the ……. chord of the circle.
(iii) The diameter of a circle pass through ……
(iv) A chord of a circle is a line segment with its end points on the ……
(v) If we join any two points on a circle by a line segment, we obtain …… of the circle.
(vi) A radius of a circle is a line segment with one end at ……. and the other end at …..
(vii) All radii of a circle are ……
(viii) The diameters of a circle are ……
(ix) The total number of diameters of a circle is …..
(x) Every point on a circle is ……. from its centre.
(xi) A chord of a circle contains exactly …… points of the circle.
(xii) A diameter is the longest …….
(xiii) Concentric circles are circles having ……
Solution:

(i) The diameter of a circle is two times its radius.

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

(iii) The diameter of a circle pass through its centre.

(iv) A chord of a circle is a line segment with its end points on the circle.

(v) If we join any two points on a circle by a line segment, we obtain chord of the circle.

(vi) A radius of a circle is a line segment with one end at centre and the other end at circle.

(vii) All radii of a circle are equal.

(viii) The diameters of a circle are concurrent.

(ix) The total number of diameters of a circle is infinite.

(x) Every point on a circle is equidistant from its centre.

(xi) A chord of a circle contains exactly two points of the circle.

(xii) A diameter is the longest chord.

(xiii) Concentric circles are circles having same centre.

Page 5

1. Explain the following:
(i) Circle
(iii) Centre
(iv) Diameter
(v) Chord
(vi) Interior of a circle.
Solution:

(i) Circle – A circle is a set of all those points in a plane whose distance from a fixed point remains constant.

(ii) Radius – The radius of a circle is the distance between the all the points of the circle to its centre.

(iii) Centre – The centre of a circle is a fixed point which is at a constant distance from all the points.

(iv) Diameter – A line segment passing through the centre of a circle, and having its end-points on the circle is
called a diameter of the circle.

(v) Chord – A line segment with its end-points lying on a circle is called the chord of the circle.

(vi) Interior of a circle – The part of a plane inside the circle consisting of all the points is called the interior of a
circle.

2. Take a point on your notebook and draw circle of radii 4 cm, 3 cm and 6.5 cm, each having the same
centre O.
Solution:

The figure given below shows circles of 4 cm, 3 cm and 6.5 cm radii having the same centre.

3. Draw a circle with centre O and any radius. Draw AC and BD two perpendicular diameters of the circle.
Join AB, BC, CD and DA.
Solution:

The figure given below shows a circle with centre O and two perpendicular diameter AC and BD.

4. Draw a circle with centre O and radius 6 cm. Mark points P, Q, R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.
Rewrite each of the following statements using the correct symbol (=, < or >):
(i) OQ …… 5 cm  (ii) OP ……. 5 cm  (iii) OR …... 5 cm.
Solution:

The figure given below shows the points P, Q and R such that
(i) P lies on the circle,
(ii) Q lies in the interior of the circle, and
(iii) R lies in the exterior of the circle.

The statements can be written as
(i) OQ < 5 cm

(ii) OP = 5 cm

(iii) OR > 5 cm

5. Take two points A and B on the page of your note book. Draw a circle with centre A which passes
through B.
Solution:

The figure given below shows the circle with A as centre and a line which passes through B.

6. Draw a semi-circle with centre O and radius 5 cm. Is the diameter that determines the semi-circle, a part
of the semi-circle?
Solution:

The figure given below shows a semi-circle with centre O and radius 5 cm.

We know that a semi-circle is the end point of a diameter which divides the circle into two equal parts.
No, the diameter does not determine the semi-circle and it is the end points of the diameter which finds the semi-
circle or a part of the semi-circle.

7. The diameter of a circle is 14 cm, find its radius.
Solution:

It is given that
Diameter of a circle = 14 cm
We know that
Radius of a circle = Diameter / 2
By substituting the values

Radius of a circle = 14/2 = 7 cm.

8. Given a circle with centre O and radius 2.5 cm, what is the length of the longest chord of the circle.
Solution:

We know that the diameter of a circle is its longest chord which is twice its radius.
So the length of the longest chord of the circle = 2 (2.5) = 5 cm.

9. Fill in the blanks:
(i) The diameter of a circle is ……. times its radius.
(ii) The diameter of a circle is the ……. chord of the circle.
(iii) The diameter of a circle pass through ……
(iv) A chord of a circle is a line segment with its end points on the ……
(v) If we join any two points on a circle by a line segment, we obtain …… of the circle.
(vi) A radius of a circle is a line segment with one end at ……. and the other end at …..
(vii) All radii of a circle are ……
(viii) The diameters of a circle are ……
(ix) The total number of diameters of a circle is …..
(x) Every point on a circle is ……. from its centre.
(xi) A chord of a circle contains exactly …… points of the circle.
(xii) A diameter is the longest …….
(xiii) Concentric circles are circles having ……
Solution:

(i) The diameter of a circle is two times its radius.

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

(iii) The diameter of a circle pass through its centre.

(iv) A chord of a circle is a line segment with its end points on the circle.

(v) If we join any two points on a circle by a line segment, we obtain chord of the circle.

(vi) A radius of a circle is a line segment with one end at centre and the other end at circle.

(vii) All radii of a circle are equal.

(viii) The diameters of a circle are concurrent.

(ix) The total number of diameters of a circle is infinite.

(x) Every point on a circle is equidistant from its centre.

(xi) A chord of a circle contains exactly two points of the circle.

(xii) A diameter is the longest chord.

(xiii) Concentric circles are circles having same centre.

10. In each of the following, state if the statement is true (T) or false (F):
(i) Every circle has a centre.
(ii) The centre of a circle is a point of the circle.
(iii) Any two radii of a circle make up a diameter.
(iv) Every chord of a circle is parallel to some diameter of the circle.
(v) A circle is symmetric about each of its diameters.
(vi) The diameter is twice the radius.
(vii) A radius is a chord of the circle.
(viii) Concentric circles have the same radii.
(ix) The nearer a chord to the centre of a circle, the longer is its length.
Solution:

(i) True.

(ii) False.

(iii) False.

(iv) False.

(v) True.

(vi) True.

(vii) False.

(viii) False.

(ix) True.

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## Mathematics (Maths) Class 6

92 videos|347 docs|54 tests

## FAQs on Circles (Exercise 14.1) RD Sharma Solutions - Mathematics (Maths) Class 6

 1. What are the properties of a circle?
Ans. A circle is a closed figure made up of all points equidistant from a fixed point called the center. The properties of a circle include: - All radii of a circle are congruent. - The diameter is twice the length of the radius. - The circumference of a circle is the distance around the circle. - The area of a circle is given by the formula A = πr^2, where r is the radius.
 2. How do you find the circumference of a circle?
Ans. The circumference of a circle can be found using the formula C = 2πr, where C is the circumference and r is the radius of the circle. Simply multiply the radius by 2π to get the circumference.
 3. What is the relationship between the diameter and radius of a circle?
Ans. The diameter of a circle is twice the length of its radius. In other words, if r is the radius of a circle, then the diameter is 2r. Conversely, if d is the diameter of a circle, then the radius is d/2.
 4. How do you find the area of a circle?
Ans. The area of a circle can be found using the formula A = πr^2, where A is the area and r is the radius of the circle. Simply square the radius and multiply it by π to get the area.
 5. What is the difference between a circle and a sphere?
Ans. A circle is a two-dimensional shape that lies completely in a plane, while a sphere is a three-dimensional shape that extends in all directions from a central point. A circle has a circumference and area, whereas a sphere has a surface area and volume.

## Mathematics (Maths) Class 6

92 videos|347 docs|54 tests

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