Find the area of the segment of a circle of radius

Solution:

From the given information, Radius of the circle = r =

   

cm

∴ OA = OB =

   

cm

   

(given)

 

As triangle OAB is an isosceles triangle, ∴ 

   

(say)

Also, we know that Sum of interior angles of a triangle is 180°,

∴ 

   

⇒

   

⇒ 

   

Therefore, triangle AOB is an equilateral triangle.

∴ AB = OA = OB =

   

cm

Area of the triangle AOB of side a=

   

=

   

=

   

=

   

   

=

   

   

Now, for Central angle of the sector AOBCA = 

   

radians

Thus, we know that area of the sector AOBCA = 

   

=

   

= 

   

=

   

   

Now, for Area of the segment ABCA = Area of the sector AOBCA – Area of the triangle AOB

=

   

   

 =