Circles Exercise 14.1 Class 6 Notes | EduRev

Mathematics (Maths) Class 6

Class 6 : Circles Exercise 14.1 Class 6 Notes | EduRev

 Page 1


 
 
 
 
 
 
                                                                              
1. Explain the following: 
(i) Circle 
(ii) Radius 
(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 
(ii) Radius 
(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 
(ii) Radius 
(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 
(ii) Radius 
(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 
(ii) Radius 
(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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