Circle

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Circle

In our daily routine, we come across many shapes that are round in shape, such as a wall clock, a wheel, sun moon, earth, coin, bangles, rings, etc. These all shapes are called a circle. 

The circle can also be imagined as a single line segment that is bent in a circular shape.

Circle Definition

  • A circle is a collection of points in a plane  from a given fixed point.

Center

  • The fixed point is called the center of the circle.

Radius

  • The fixed distance from the center is called the radius of a circle.

Chord: 

  • A line segment joining any two points on the circle is called a chord. 

Diameter: 

  • A chord that passes through the center of the circle is called the diameter of a circle.
  • Also diameter is the longest chord and can be expressed as 2r where r is the radius of a circle. 
  • There are infinite numbers of diameter in a circle.

Secant: 

  • A chord that intersects the circle in two points is called a secant.

Tangent:

  •  A line that touches a circle in one point is called tangent to the circle. 
  • And that point is called the point of contact.

Arc :

  •  A piece of circle between two points is called an arc.

Circumference:

  • The length of the complete circle is called the circumference of a circle. 
  • It is also said to be the perimeter of the circle.
  •  The circumference of a circle = 2πr, where r is the radius of a circle.

Segment:

  • The region between the chord and the arc is called the segment of the circle.
  • The segment containing the minor arc is called the minor segment and the segment containing the major arc is called the major segment.

Sector: 

The region between the arc at the two radii is called the sector. 

TO REMEMBER:

Properties of Circle

  • Circles with the same radii are said to be congruent.
  • The longest chord of a circle is the diameter of a circle.
  • The diameter of a circle is double the radius.
  • The diameter divides the circle into two equal semicircles.
  • The radius that is drawn perpendicular to the chord bisects the chord
  • A circle can be inscribed in a square, triangle or a  kite

Formulas For Circle

Diameter d : 

The diameter of a circle is twice the radius of a circle.

d = 2r

Circumference: 


The outer boundary of the circle is the circumference of the circle. The formula for circumference is given by-

C = πd = 2πr 

Area: 

Area of the circle is defined as the space occupied by the circle. The formula for area is given by

A =πr2

Example 1:

 Find the Area and the Circumference of a circle whose radius is 7 cm. (Take the value of π = 22/7)

Solution-

Given radius r  = 7 cm.

Area A = π r× r

= 22/7  × 7 x 7

Area  = 154 Sq.cm 

Circumference C = 2πr

     = 2  x 22/7 x 7 

Circumference =  44 cm


Example 2 :

 If the diameter of a circle is 12cm. Then find its area.

Solution:

Given, diameter d = 12cm

So, radius r = d /2 

= 12/2 

= 6cm

Hence, area A = πr^2

          A = π x (6)^2

  = 3. 14 x 36

          A = 113.04 cm2

QUIZ TIME:

https://forms.gle/N8Zwge4ty8qs6Zv19

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