Q. 284.1( 16 Votes )

A chord PQ of a c

Answer :

Let r be the radius of the circle = 10 cm

The figure is given below:



Angle subtended at the center of the sector = θ = 60°


OP = OQ = r = radius


In triangle POQ, POQ = 60°, OPQ = OQP = ϕ


Since, sum of all interior angles of a triangle is 180°


θ+ ϕ + ϕ = 18o°


60° + 2 ϕ = 180°


2 ϕ = 180° - 60° = 120°


ϕ = 60°


Each angle is of 60° and hence the triangle POQ is an equilateral triangle.


Now, Area of the minor segment = Area of the sector POQR – Area of triangle POQ


Angle subtended at the center of the sector =60°


Angle subtended at the center (in radians) = θ = 60π/180 = π/3


Area of sector POQR of a circle = (1/2) × r2 × θ


= (1/2) × 100 × (π/3)


= 50π/3


= (50 × 3.14)/3


= 52.33 cm2


Area of the equilateral triangle POQ = (√3/4) × (Side)2


= (√3/4) × (10)2


= 25√3 cm2


= 43.30 cm2


Area of minor segment = Area of the sector POQR – Area of triangle POQ = (52.33 – 43.30) cm2


= 9.03 cm2


Now, area of the circle = πr2 = 3.14 × 100 = 314 cm2


Area of the major segment = Area of circle – Area of the minor segment = (314 – 9.03) cm2 = 304.97 cm2


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