Note on Circle

• Note
• Things to remember
• Exercise
• Quiz

Circle

A circle is the set of points in a plane that are in same distant from a center. A circle is named by its center.

The distance from the centre of the circle to any point on a circle is called the radius of the circle.

In the given figure, O is the centre and OA is a radius of the circle.

Diameter

The diameter of a circle is the distance across a circle through the center.

In the figure, BA is a diameter.

Chord

A chord is a line segment that joins two endpoints that lie on a circle. A circle has many different chords.

In the figure, AB is a chord of the circle.

Circumference and Arc of a circle

Circumference is the distance once around the circle. And a part of the circumference is called an Arc.

In the given figure, the smaller part CXB is known as the minor arc and the greater part CYB is known as the major arc.

Sectors of a circle

A slice of a pizza can be known as a sector of a circle. There are especially two types of a sector in circle: Quadrant and Semicircle.

A quarter of a circle is called a Quadrant.

Half a circle is called a Semicircle.

Segment of a circle

A chord divides the circle into two parts and the parts made by a chord is called a Segment.

The smaller part is called the minor segment and the other part is called the major segment.

Inscribed angle

An inscribed angle is an angle formed by two chords in a circle which has a common endpoint. This common endpoint forms the vertex of the inscribed angle and the corresponding arc is called the intercepted arc. In the figure, ABC is an inscribed angle and AC is called an intercepted arc.

Circles Intersecting

Two circles may intersect in two imaginary points that may a single degenerate point or two distinct points.

In the figure, two circle are intersect where, AB is the common chord of the circles with centre O and P.

Concentric Circles

Concentric circles are simply a circles with a same distance apart all the way aroundwith a common center.

In the figure, three circles have the same centre O, so the circles are concentric.

A cyclic quadrilateral is a quadrilateral whose all polygon vertex touches the circumference of a circle.

In the above figure, only in fig (iii) ABCD is cyclic quadrilateral and vertices A, B, C and D are concyclic.

Secant

Secant is a line that intersects the circle at two distinct points.

In the figure, the line XY is a secant.

Tangent

A line that touches a circle at just one point is a tangent.In the figure, AB is a tangent to the circle at C. The point C is called the point of contact.

At most two tangent can be drawn to the circle from an external point.

• A circle is the path of all the points that are equidistant from a fixed point.
• The diameter of a circle is the line segment joining two points on the circle and passing through the centre of the circle.
• Diameter is the longest chord of the circle.
• The smaller part is known as the minor arc and the greater part is known as the major arc.
• A diameter of a circle divides it into two equal parts. Each part is called a Semicircle.
• A Chord of a circle divides the circular region into two parts. Each part is called a segment of the circle.
• Two circles are said to be intersecting circles if they have one and only one common chord.
• Two or more circles having the same centre are called concentric circles.
.

Very Short Questions

Solution:

Here,

$$\pi$$= 3.14

Diameter of circle(d) =10 inch

Circumference of circle (c)= ?

By using formula,

c = $$\pi$$ d

= 3.14×10 inch

= 31.4 inch

Solution:

Here,

$$\pi$$= 3.14

Radius of a circle(r)=12 m

Circumference of circle (c)= ?

By using formula,

c =2$$\pi$$ r

=2×3.14×12 m

=75.36 m

Solution:

Here,

$$\pi$$= 3.14

Diameter of a circle(d) = 18 ft

Circumference of circle(c )= ?

By using formula,

c = $$\pi$$d

=3.14 × 18bft

= 56.52 ft

Solution:

Here,

$$\pi$$= 3.14

Circumference of circle(C)=65.94 ft

We know that,

C=2$$\pi$$r

or, 65.94=2×3.14×r

or, 6.28×r=65.94

or, r=$$\frac{65.94}{6.28}$$

or, r=10.5

∴ Radius(r)= 10.5 ft

Solution:

Here,

$$\pi$$=$$\frac{22}{7}$$

Radius of a circular stadium(r) = 100m

Circumference (C)=?

We know that,

C = 2$$\pi$$r

=2×3.14×100

=628m

∴ Radius of a circular stadium is 628m

Solution:

Here, $$\pi$$=$$\frac{22}{7}$$

Radius of a circle(r)= 3 cm

Area of a circle(A)=?

By using formula,

A=$$\pi$$r2

=3.14×(3)2

=28.26 cm2

Hence, Area of a circle = 28.26 cm2

Solution:

Here,

$$\pi$$=3.14

Diameter of a circle(d)= 5 cm

Radius of a circle(r)=$$\frac{d}{2}$$=$$\frac{5}{2}$$=2.5 cm

Area of a circle(A)=?

By using formula

A=$$\pi$$r2

=3.14×(2.5)2

=19.625 cm2

Hence, Area of a circle(A)=19.625 cm2

Solution:

Here,

$$\pi$$= 3.14

Radius of a circle(r)=8 ft.

Area of a circle(A)=?

By using formula,

A=$$\pi$$r2

=3.14×(8)2

=200.96 ft2

Hence, Area of a circle(A)=200.96 ft2

Solution:

Here,

$$\pi$$=3.14

Diameter of a circle=(d)=12 inch

Radius of a circle(r)=$$\frac{d}{2}$$

=$$\frac{12}{2}$$

= 6 inch

Area of a circle(A)=?

By using formula,

A=$$\pi$$r2

=3.14×(6)2

=113.04 inch2

Hence, Area of a circle(A)=113.04 inch2

Solution:

Here,

$$\pi$$= 3.14

Diameter of a circle(d)=15 mm

Radius of a circle(r)=$$\frac{d}{2}$$

=$$\frac{15}{2}$$

=7.5 mm

Area of a circle(A)=?

By using formula

A = $$\pi$$r2

=3.14×(7.5)2

=176.625 mm

Hence, Area of a circle(A)=176.625 sq.mm

Solution:

Here,

$$\pi$$= 3.14

Diameter of a circle(d)=22 cm

Radius of a circle(r)=$$\frac{d}{2}$$

=$$\frac{22}{2}$$

=11 cm

Area of a circle(A)= ?

By using formula,

A= $$\pi$$r2

=3.14×(11)2

=379.94 cm2

Hence, Area of a circle (A)=379.94 cm2

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7cm
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12.5cm
11cm
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12.7cm
18.2cm

50,000
45,000
48,000
55,000

6.16km
12km
5km
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85cm
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81cm
88cm
85cm
87cm

9087m2
9845m2
9765m2
9856m2

5544m2
5588m2
5548m2
5545m2

98.56m2
99.82m2
95.25m2
97.67m2

20m
12m
16m
14m

1.5m2
3.5m2
4.5m2
2.5m2

12cm
11cm
5cm
7cm

176m
175m
155m
178m

44cm
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45cm
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Hi ande

unknown

how to find diameter if circumfernce is given??plz reply fastet