Question

a chord of a circle of radius 21cm make an angel 120°find the area of the minor segment
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Answer 1

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

PLZ MARK AS BRAINLIST ANSWER.

Answer 2

Answer:

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