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
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.
Given that,, radius, cm
Area of the sector
Area of minor segment Area of sector Area of
Area of the circle
Area of major segment Area of the circle Area of minor segment
(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
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:
Note: If the height of the segment is less of radius of the circle, then .
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.
Given that, cm, cm
Find the area of the segment whose chord is cm, and whose height is cm.
Given that cm, cm