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A segment is a portion of a circle which cut off by a straight line not passing through the centre. The segment, smaller than the semi-circle is called the minor segment and the segment larger than the semi-circle is called the major segment.
(a) Area of the minor segment when angle  and radius  are given:
Area of segment  Area of sector   Area of 
Now area of major segment  Area of circle  Area of minor segment
Example:
A chord  of a circle of radius  cm makes an angle of  at the centre of the circle. Find the area of the major and minor segment.
Solution:
Given that, , radius,  cm
 Area of the sector  
 Square cm
 Area of  
 Square cm
Area of minor segment  Area of sector   Area of 
 Square cm
Area of the circle 
 Square cm
Area of major segment  Area of the circle  Area of minor segment
 Square cm.
(b) Area of segment when height and length of the chord of the segment are given:
Let  radius of the circle
 height of the segment
 length of the chord
We note that  is a right triangle; the hypotenuse is  and the other two sides are  and 
 By Pythagorean Theorem
Solving for ,  and , we obtain the following formulas
 --- (1)
 --- (2)
 --- (3)
Note:
 Gives the height of the major segment
 Gives the height of the minor segment
Many formulas are given for finding the approximate area of a segment. Two of the common methods are:
Method-I: 
Note: If the height of the segment is less  of radius of the circle, then  .
Method-II: 
Example:
If the chord of the segment of a circle is  cm and the height of the segment is  cm, find the radius of the circle.
Solution:
Given that,  cm,  cm
 
 cm
Example:
Find the area of the segment whose chord is cm, and whose height is  cm.
Solution:
Given that  cm,  cm
 
 Square cm.
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