The students will get a brief idea about the important concepts which are covered in this chapter using the PDF of solutions. This exercise has problems based on the steps followed to draw a circle and methods of determining angles and diameters. The students can refer to the solutions while solving problems in the RD Sharma textbook to gain expertise in the subject. To get a better conceptual knowledge of this chapter, the students can download RD Sharma Solutions Class 6 Maths Chapter 14 Circles Exercise 14.1 PDF, which is provided here.
RD Sharma Solutions for Class 6 Maths Chapter 14: Circles Exercise 14.1
Access answers to Maths RD Sharma Solutions for Class 6 Chapter 14: Circles Exercise 14.1
Exercise 14.1 page: 14.4
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 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 in your notebook and draw circles 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, 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.
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 notebook. Draw a circle with centre A which passes through B.
Solution:
The figure given below shows the circle with A as a 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.
Comments