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Question

A chord PQ of a circle of radius 10 cm subtends an angle of 60 at the centre of the circle. Find the area of major and minor segments of the circle.


Solution

Area of sector formed by the arc =θ360×πr2=60360×227×102=110021=52.38 cm2

In OAB, let OM be bisector of AB,

AOM=BOM

Let OM be x cm

In OMA,

OMOA=cos 30ox10=32x=53=8.66 cmOM=8.66 cm

In OMA,

AMOA=sin 30oAM10=12AM=5 cmAB=2×AM=2×5=10 cm

Area of OAB =12×OM×AB=12×8.66×10=43.3 cm2

Area of minor segment =  Area of sector formed by the arc - Area of OAB=52.3843.3=9.08 cm2

Area of major segment = Area of circle - Area of minor segment 

=πr29.08=3.14×10×109.08=3149.08=304.92 cm2


Mathematics
Secondary School Mathematics X
Standard X

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