10.1 Circles I


10.1 Circles I
 
10.1.1 Parts of a Circle
1. A circle is set of points in a plane equidistant from a fixed point.

2. 
Parts of a circle:
(a)    The centre, O, of a circle is a fixed point which is equidistant from all points on the circle.




(b)
   A sector is the region enclosed by two radii and an arc.




(c)
    An arc is a part of the circumference of a circle.


(d)
   A segment is an area enclosed by an arc and a chord.
 

10.1.2 Circumference of a Circle
   circumference=πd,      where d=diameter                            =2πr,     where r=radius                                    π(pi)= 22 7      or   3.142
Example:
Calculate the circumference of a circle with a diameter of 14 cm. ( π = 22 7 )

Solution
:
Circumference = π × Diameter = 22 7 × 14 = 44 cm



10.1.3 Arc of a Circle
The length of an arc of a circle is proportional to the angle at the centre.
      Length of arc Circumference = Angle at centre 360 o        
Example:
 
Calculate the length of the minor arc AB of the circle above. ( π = 22 7 )

Solution
:
Length of arc Circumference = Angle at centre 360 o Length of arc A B = 120 o 360 o × 2 × 22 7 × 7 = 14 2 3 cm


10.1.4 Area of a Circle

   Area of a circle = π× ( radius ) 2                                =π r 2
 
Example:
Calculate the area of each of the following circles that has
(a) a radius of 7 cm,
(b)   a diameter of 10 cm.
( π = 22 7 )  

Solution
:
(a)
Area of a circle = π r 2 = 22 7 × 7 × 7 = 154 cm 2

(b)
Diameter of circle = 10 cm Radius of circle = 5 cm Area of circle = π r 2 = 22 7 × 5 × 5 = 78.57 cm 2


10.1.5 Area of a Sector
The area of a sector of a circle is proportional to the angle at the centre.
      Area of sector Area of circle = Angle at centre 360 o      

Example
:







Area of sector A B C = 72 o 360 o × 22 7 × 7 × 7 = 30 4 5 cm 2


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