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Question

A circle having radius 4 cm contains a chord of length 4 cm and subtends an angle of 60 degrees. Find the area of the minor segment of the chord.


A

2

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B

1.5

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C

3

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D

None of these

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Solution

The correct option is B

1.5


Area of sector POQ

=60360×π42=8.4 cm2

In triangle OSQ which is right angled at S,
OQ2=SQ2+OS2

16=4+OS2
OS=23

Area of triangle POQ
=12 ×base×height
=12×4×23
=6.9 cm2

Now,
Area of segment PSQR = Area of sector POQ - Area of triangle POQ
=8.46.9 cm2
=1.5 cm2


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