Question

chord of circle of radius 15cm substends an angel of 60° at centre.Find the area of the corresponding minnor and major segments of circle(use π=3.14 & √3=1.73)​

Answer 1

The area of the corresponding minor and major segments of the circle are  20.44 cm²  and 686.06 cm²  respectively.

Step-by-step explanation:

The radius of the circle, r = 15 cm

The angle subtended by the chord and the radius of the circle at the centre, θ = 60°.

Case 1: Area of the minor segment PRQ

The area of the sector OQRP is given by,

= πr² * [θ/360°]

= 3.14 * 15 * 15 * [60°/360°]

= 117.75 cm²

Consider ∆ POQ, we have  

OP = OQ = 15 cm ...... [radius of the circle]

So, ∠OPQ = ∠OQP ….. [angles opposite to equal sides are equal]

∴ ∠OPQ + ∠OQP + ∠POQ = 180°

⇒ 2 * angle OPQ = 180° - 60° = 120°

⇒ angle OPQ = angle OQP = 120°/2 = 60°

∴ ∆ POQ is an equilateral triangle with each angle 60°

∴ Area of equilateral triangle POQ = $\frac{\sqrt{3}}{4}$ * side² =$\frac{1.73}{4}$ * 15² = 97.31 cm²

Thus,  

The area of the minor segment PRQ of the circle is given by,

= [Area of the sector OQRP] – [Area of equilateral triangle POQ]  

= 117.75 cm² - 97.31 cm²

= 20.44 cm²

Case 2: Area of major segment QSP

Area of the circle = πr² = 3.14 * 15² = 706.5 cm²

Thus,

The area of the major segment QSP is given by,

= [Area of the circle] – [Area of the minor segment PRQ]  

= 706.5 - 20.34

= 686.06 cm²

-------------------------------------------------------------------------------------

Also View:

Find the area area of minor segment of circle of radius 42 cm if length of the corresponding arc is 22 cm ?

https://brainly.in/question/13748371

If a chord of a circle of radius 28 cm makes an angle of 90 ° at the centre, then the area of the major segment is ?

https://brainly.in/question/9594546

Show all the class10 formula of chapter 12 area related to circles

https://brainly.in/question/4882750