Question

a chord of a circle of radius 21 cm makes an angle 120° at the centre of the circle. find the area of the segment so formed.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The area of segment formed would be 271 cm²

1) Let the center of circle be O and the chord be AB.

2) AB makes an angle of 120 at the center of circle with radius 21 cm

3) The area of segment AB thus formed would be equal to Area of sector AOB - Area of Triangle AOB

4) The area of sector AOB would be  πr²*(θ/360)

Here, the given angle is 120.

Hence the area is π(21)²*(120/360) = π*21*21*1/3

The area of Sector would be 462 cm²

5) In the triangle AOB, the top angle is 120 and two sides are 21 cm

6) The area of triangle can be calculated by using

Area = (side1 *side2* sin θ)/2

Area = (21*21* sin120)/2

Area = (21*21*√3)/2

7)  Hence, the area of segment would be π*21*21*1/3 - (21*21*√3)/2

= 21*21*( π/3 - √3/2)

= 271 cm²