A chord of a circle, 7 cm long subtends an angle of 60° at the centre of the circle. Detemine the area correct to 2 decimal places, of the major segment of the circle.

Question

A chord of a circle, 7 cm long subtends an angle of 60° at the centre of the circle. Determine the area correct to 2 decimal places, of the major segment of the circle.

Answer 1

θ =^π/₃                                         θ=360−60=300
θ =2π−^π/₃                                   arc length, b = ^θ/₃₆₀ . 2πr
   =1²/₃π                                     chord= radius = 7cm
area=½θr²                                                 b = 300 × 2 × 22 × 7
        where θ is in radians                                360            7
=½ × ⁵/₃π × 7 × 7                                =36²/₃cm
=128.28cm²                                    area=½b.r
                                                            =½ × 36²/₃ × 7
                                                            =128¹/₃cm²
                                                            ≈128.33cm²