Note on Circle

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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.

Circle

Radius

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.

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Diameter

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

In the figure, BA is a diameter.

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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.

Chord

 

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.

Arc of a circle

 

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.

.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.

Segment of a circle

 

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.

inscribed circle

 

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.

intersecting circles

 

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.

concertric circle

 

Cyclic Quadrilaterals

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

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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.

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.

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

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  • 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.
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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

Radius(r)=?

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

0%
  • Find the radius of a circle whose circumference is 44cm.

    7cm
     8cm
     9cm
     12cm
  • A wire  in the form of the rectangle 18.7 cm long and 14.3 cm wide is reshaped and bent into the form of a circle. Find the radius of the circle formed.

     12.5cm
      11cm
     10.5cm
     11.5cm
  • Find the diameter of a circle whose circumference is 57.2.

    15.5cm
    17cm
     12.7cm
     18.2cm
  • The diameter of the wheel of a car is 77cm. How many revolutions will it make to travel 121 km?

    50,000
    45,000
    48,000
    55,000
  • Find the distance covered by the wheel of a car in 2000 rotations if the diameter of the wheel is 98cm.

    6.16km
    12km
     5km
    7km
  • Find the circumference of a circle whose radius is 14cm.

     85cm
     88cm
     84cm
     87cm
  • Find the circumference of a circle whose diameter is, 28cm.

     81cm
     88cm
     85cm
     87cm
  • Find the area of the circular region whose radius is, 56m.

     9087m2
    9845m2
    9765m2
    9856m2
  • Find the area of a circular park whose circumstance is 264m.

    5544m2
    5588m2
    5548m2
    5545m2
  • The circumference of a circle is 35.2m. Find its area.

    98.56m2
    99.82m2
    95.25m2
    97.67m2
  • The area of a circle is 616m2.Find its radius.

    20m
    12m
    16m
    14m
  • Find the area of a circular region whose diameter is 2.1.

    1.5m2
    3.5m2
    4.5m2
    2.5m2
  • The area of a circle is 154cm2.Find its circumference.

    12cm
    11cm
    5cm
    7cm
  • Find the circumstances of a circle whose area is 2464m2.

     176m
     175m
     155m
     178m
  • Find the circumference of a circle whose radius is 7cm.

     44cm
     54cm
     47cm
     45cm
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DISCUSSIONS ABOUT THIS NOTE

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Sushrut

Hi ande


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unknown

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


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Radiud

A wheel goes 110m far in 5 revolutions. Find the radius


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