RS Aggarwal Solutions: Circles | Mathematics (Maths) Class 6 PDF Download

 Page 1


Points to Remember :
Circle. It is the set of all those points in a plane whose distance from a fixed point remains constant.
The fixed point is called the centre of the circle and the constant distance is called the radius of the
circle.
All the radii of a circle are equal.
Diameter of a circle
A line segment passing through the centre of circle and having its end
points on the circle is diameter of the circle.
Diameter = 2 × radius
Chord of a circle. A line segment with its end points
lying on a circle is called the chord of the circle.
Secent of a Circle. A line passing through a circle and
intersecting the circle at two points is called a secent of
the circle.
Circumference of a circle. The perimeter of a circle is
called the circumference of the circle
Semi-circle. The end points of a diameter of a circle
divide the circle into two parts ; each part is called a
semi-circle.
Arc. Any part of a circle is called an arc of the circe.
Segments of a Circle
A chord AB of a circle divides the circular region into
two parts. Each part is called a segment of the circle.
The segment containing the centre of the circle is called
the major segment, while the segment not containing the
centre is called the minor segment of the circle.
Sector of a Circle. The area bounded by an arc and the
two radii joining the end points of the arc with the centre,
is called a sector. If the sector is formed by a major arc
then it is called a major sector. If the sector is formed by
a minor arc, it is called a minor sector.
Concentric circles. Two or more circles with the same
centre are called concentric circles.
Page 2


Points to Remember :
Circle. It is the set of all those points in a plane whose distance from a fixed point remains constant.
The fixed point is called the centre of the circle and the constant distance is called the radius of the
circle.
All the radii of a circle are equal.
Diameter of a circle
A line segment passing through the centre of circle and having its end
points on the circle is diameter of the circle.
Diameter = 2 × radius
Chord of a circle. A line segment with its end points
lying on a circle is called the chord of the circle.
Secent of a Circle. A line passing through a circle and
intersecting the circle at two points is called a secent of
the circle.
Circumference of a circle. The perimeter of a circle is
called the circumference of the circle
Semi-circle. The end points of a diameter of a circle
divide the circle into two parts ; each part is called a
semi-circle.
Arc. Any part of a circle is called an arc of the circe.
Segments of a Circle
A chord AB of a circle divides the circular region into
two parts. Each part is called a segment of the circle.
The segment containing the centre of the circle is called
the major segment, while the segment not containing the
centre is called the minor segment of the circle.
Sector of a Circle. The area bounded by an arc and the
two radii joining the end points of the arc with the centre,
is called a sector. If the sector is formed by a major arc
then it is called a major sector. If the sector is formed by
a minor arc, it is called a minor sector.
Concentric circles. Two or more circles with the same
centre are called concentric circles.
        Q. 1. Take a point O on your note book and
draw circles of radii 4 cm., 5.3 cm. and
6.2 cm., each having the same centre.
Sol. Method :
Take a point O on the paper as shown in
the figure. With the help of the rular,
open out compasses in such a way that
the distance between the metal point and
pencil point is 4 cm. Take the compasses
in the same position and put its metal
point at O and draw the circle.
Remove the compasses and again open
out the compasses in such a way that
the distance between the metal point and
pencil point is 5.3 cm. Taking O as the
centre, draw another circle. Again
remove the compasses and similarly
draw the third circle with radius 6.2 cm.
Then the required circles are as shown
in the figure which have radius OA = 4
cm., OB = 5.3 cm. and OC = 6.2 cm.
Q. 2. Draw a circle with centre C and radius
4.5 cm. Mark points P, Q and R such
that P lies in the interior of the circle, Q
lies on the circle and R lies in the exterior
of the circle.
Sol. Method : Take a point C on the paper.
With the help of the rular, open out the
compasses in such a way that the
distance between its metal point and
pencil point is 4.5 cm. Take the
compasses in the same position and put
its metal point at C and draw the circle.
Mark points P, Q and R as shown in the
figure as required.
Q. 3. Draw a circle, with centre O and radius
4 cm. Draw a chord AB of the circle.
Indicate by marking point X and Y, the
minor are AX B and the major are AYB.
Sol. Method : Take a point O on the paper.
With the help of the rular, open out the
compasses in such a way that  the
distance between the metal point and
pencil point is 4 cm. Take the compasses
in the same position and put the metal
point at O and draw the circle.
Take A and B any points on the circle
and join AB. Then AB is the chord of the
Page 3


Points to Remember :
Circle. It is the set of all those points in a plane whose distance from a fixed point remains constant.
The fixed point is called the centre of the circle and the constant distance is called the radius of the
circle.
All the radii of a circle are equal.
Diameter of a circle
A line segment passing through the centre of circle and having its end
points on the circle is diameter of the circle.
Diameter = 2 × radius
Chord of a circle. A line segment with its end points
lying on a circle is called the chord of the circle.
Secent of a Circle. A line passing through a circle and
intersecting the circle at two points is called a secent of
the circle.
Circumference of a circle. The perimeter of a circle is
called the circumference of the circle
Semi-circle. The end points of a diameter of a circle
divide the circle into two parts ; each part is called a
semi-circle.
Arc. Any part of a circle is called an arc of the circe.
Segments of a Circle
A chord AB of a circle divides the circular region into
two parts. Each part is called a segment of the circle.
The segment containing the centre of the circle is called
the major segment, while the segment not containing the
centre is called the minor segment of the circle.
Sector of a Circle. The area bounded by an arc and the
two radii joining the end points of the arc with the centre,
is called a sector. If the sector is formed by a major arc
then it is called a major sector. If the sector is formed by
a minor arc, it is called a minor sector.
Concentric circles. Two or more circles with the same
centre are called concentric circles.
        Q. 1. Take a point O on your note book and
draw circles of radii 4 cm., 5.3 cm. and
6.2 cm., each having the same centre.
Sol. Method :
Take a point O on the paper as shown in
the figure. With the help of the rular,
open out compasses in such a way that
the distance between the metal point and
pencil point is 4 cm. Take the compasses
in the same position and put its metal
point at O and draw the circle.
Remove the compasses and again open
out the compasses in such a way that
the distance between the metal point and
pencil point is 5.3 cm. Taking O as the
centre, draw another circle. Again
remove the compasses and similarly
draw the third circle with radius 6.2 cm.
Then the required circles are as shown
in the figure which have radius OA = 4
cm., OB = 5.3 cm. and OC = 6.2 cm.
Q. 2. Draw a circle with centre C and radius
4.5 cm. Mark points P, Q and R such
that P lies in the interior of the circle, Q
lies on the circle and R lies in the exterior
of the circle.
Sol. Method : Take a point C on the paper.
With the help of the rular, open out the
compasses in such a way that the
distance between its metal point and
pencil point is 4.5 cm. Take the
compasses in the same position and put
its metal point at C and draw the circle.
Mark points P, Q and R as shown in the
figure as required.
Q. 3. Draw a circle, with centre O and radius
4 cm. Draw a chord AB of the circle.
Indicate by marking point X and Y, the
minor are AX B and the major are AYB.
Sol. Method : Take a point O on the paper.
With the help of the rular, open out the
compasses in such a way that  the
distance between the metal point and
pencil point is 4 cm. Take the compasses
in the same position and put the metal
point at O and draw the circle.
Take A and B any points on the circle
and join AB. Then AB is the chord of the
circle. Mark points X and Y on the circle
as shown. Then arc AXB and arc AYB
are the required minor and major arcs
respectvely.
Q. 4. Which of the following statements are
true and which are false ?
(i) Each radius of a circle is also a chord of
the circle.
(ii) Each diameter of a circle is also a chord
of the circle.
(iii) The centre of a circle bisects each chord
of the circle.
(iv) Secent of a circle is a segment having
its end points on the circle.
(v) Chord of a circle is a segment having its
end points on the circle.
Sol. (i) False (ii) True
(iii) False (iv) False
(v) True.
Q. 5. Draw a circle with centre O and radius
3·7 cm. Draw a sector having the angle
72º.
Sol. Steps of construction :
(i) With centre O and radius 3·7 cm, draw a
circle.
(ii) Take a point A on the circumference of
the circle.
(iii) Join OA.
(iv) At O, draw another radius OB such that
AOB = 72º with the help of protractor.
Then sector AOB is the required one.
Q. 6. Fill in the blanks by using <, >, = or 
(i) OP........OQ, where O is the centre of
the circle, P lies on the circle and Q is in
the interior of the circle.
(ii) OP........OR, where O is the centre of the
circle, P lies on the circle and R lies in
the exterior of the circle.
(iii) Major arc..........minor arc of the circle.
(iv) Major arc........semicircumference of the
circle.
Sol. (i) > (ii) < (iii) > (iv) >.   Ans.
Q. 7. Fill in the blanks :
(i) A diameter of a circle is a chord
that..........the centre.
(ii) A radius of a circle is a line segment with
one end point.........and the other end
point......... .
(iii) If we join any two points of a circle by a
line segment, we obtain a..........of the
circle.
(iv) Any part of a circle is called an...........of
the circle.
(v) The figure bounded by an arc and the
two radii joining the end points of the arc
with the centre is called a...........of the
circle.
Sol. (i) Passes through (ii) at the centre, on
the circle (iii) chord (iv) arc (v) sector.
Ans.