A chord of circle of radius 12 cm subtends an angle of 120 at centre.Find the area of the segment of circle.plz show the answer in 2 ways: one if we dont know the value of sin 120 ,two we know the value.

If the angle subtend at the centre by the chord is 120, the area of the segment will be area of the sector – area of the triangle subtend at the centre.
Area of sector= pi(r)². (120/360)

Area of triangle= 1/2r² SinA. where A is the centre. So, A=120
OR
Area of triangle ABC(where A is the centre, b and C lie on the circle)
So, a perpendicular AD dropped from A on BC will bisect it. So, in rt angled triangle ADC, Sin C= Sin 30= AD/ AC
So, AD= AC sin 30= r/2
And similarily, DC= AC cos 30= r.

Use the dimensions of the three sides of both the right angled triangles to find the area of triangle ABC.(using Heron’s formula or Area= ½ b*h)