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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.

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.

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
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\sqrt{3}/2.

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)

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