1.
Mathematics
Art Integrated Activity

2.
JAWAHAR
NAVODAYA
VIDYALAYA
KHEDGAON,
NASHIK
2022-23
Name- Swadesh Shivaji Jadhav
Class – 10
Div - 'A'
Roll no. - 1035/35
Sub - Mathematics
Guided By- A. D. Shinde sir

3.
contents
Circle and its related terms .
Area of a circle .
Perimeter of a circle
Sector of a circle and its area .
Segment of a circle and its area
Areas of combinations of plane figures

4.
• Circle and its related terms
Circle – Definition
The collection of all the points in a plane which are at
a fixed distance from in the plane is called a circle .
Or
A circle is a locus of a point which moves in a plane
in such a way that its distance from a fixed point
always remains same.

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Terms Related to Circles

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1. Radius – The line segment joining the centre
and any point on the circle is called a radius of
the circle .

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2. A circle divides the plane on which it lies into
three parts .
They are
• The Interior of the circle .
• The circle . Exterior
• The exterior of the circle .
Here , in the given fig. We can see that point B is in the cricle, point A
is on the circle and point A is in exterior of the circle

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3. Chord – if you take two points P and Q on a circle , then the line
segment PQ is called a chord of the circle
4. Diameter – the chord which passes through the centre of the circle
is called a diameter of the circle
Here in the given fig. OR is the diameter of the
circle and PR is the chord of the circle .
Note :- A diameter of a circle is the longest
chord of the circle

9.
• Arc, Segment and Sector of a Circle
1. Arc of a Circle
The arc of a circle is defined as the part or segment of the
circumference of a circle. If the length of an arc is exactly half of
the circle, it is known as a semicircular arc.
Here in the given fig. ACB is the
major arc because it is the longer one
whereas AB is the minor arc of the
given circle.

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2.Segment -
the region between a chord and either of its arc is called a segment of the circle.

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3. Sector -
the region between two radii, joining the centre to the end points of the arc is called a
sector
Here in the given fig. you find that
minor arc corresponds to minor
sector and major arc
corresponds to major sector.

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• Circumference of a Circle
The perimeter of a circle is its boundary or the complete arc
length of the periphery of a circle.
We know that circumference of a circle bears a constant ratio with its
diameter .
Circumference = 2𝜋r

13.
• Area of a Circle
Area of a circle is 𝜋rxr, where r is the radius of the circle. We have verified
it in class 7, by cutting a circle into a number of sectors and rearranging
them as shown in fig.

14.
• Area and circumference of semicircle

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• Area of a Sector
• Following are some important points to remember
• 1.A minor sector has an angle 𝜃, (say), subtended at the
centre of the circle , whereas a major sector has no angle .
• 2.The sum of arcs of major and minor sectors of a circle
is equal to the circumference of the circle.
• 3.The sum of the areas of major and minor sectors of a
circle is equal to the areas of the circle.
• 4.The boundary of a sector consists of an arc of the circle
and the two radii.

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• Area of a Sector

17.
Area of a segment of a circle