A chord of a circle of radius subtends an angle of at the centre. Find the area of the corresponding segment of the circle. (Use and )
Step 1: Find the area of minor sector of the circle
Draw a perpendicular on chord and it will bisect chord .
Area of triangle
Area of segment=Area of the sector -the area of a triangle
The area of the minor sector
Step 2: Find the area of
From the ,
We know that bisects .
So, the area of
Here, base and
So, area of
Step 3: Find the area of Minor segment
Step 4: Find the area of major segment
Area of major segment Area of circle Area of minor segment
Hence, the area of the corresponding segment of the circle are and