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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 cm2

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B

1.5 cm2

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C

3 cm2

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D

0.5 cm2

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Solution

## The correct option is B 1.5 cm2 Area of sector POQ =θ360°×πr2 =60°360°×π(4)2=8.4 cm2 In triangle OSQ which is right angled at S, OQ2=SQ2+OS2 ⇒16=4+OS2 OS=2√3 Area of triangle POQ =12 ×base×height =12×4×2√3 =6.9 cm2 Now, Area of segment PSQR = Area of sector POQ - Area of triangle POQ =8.4–6.9 cm2 =1.5 cm2

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