Given,
Radius of the circle, r = 5√2 cm = OA = OB
Length of the chord AB = 10 cm
In triangle OAB,
We see that the Pythagoras theorem is satisfied.
So, OAB is a right angle triangle.
Angle subtended by the chord with the centre of the circle, θ = 90°
Area of minor segment = area of sector – area of triangle
= θ/360 × πr2 – ½ x r2 sin θ
= 90/360 × (3.14) 5√22 – 1/2 x (5√2)2 sin 90
= [1/4 x 3.14 x 25 x 2] – [1/2 x 25 x 2 x 1]
= 25(1.57 – 1)
= 14.25 cm2
Area of circle = πr2 = 3.14 x (5√2)2 = 3.14 x 50 = 14.25 cm2
Thus, Area of major segment = Area of circle – Area of minor segment
= 157 – 14.25
= 142.75 cm2
