7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.
(Use and )
For the area of the segment, we need the area of sector and area of the associated triangle.
So, the area of the sector is :
Now, consider the triangle:-
Draw a perpendicular from the centre of the circle on the base of the triangle (let it be h).
Using geometry we can write,
Thus the area of the triangle is :
Hence the area of segment is:.