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. [Take π = 22/7 and √3=1.73]
1.46 cm2
Area of sector POQ
=θ360°×πr2
=60°360°×π(4)2=8.38 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
=6.92 cm2
Now,
Area of segment PSQR = Area of sector POQ - Area of triangle POQ
=8.38–6.92 cm2
=1.46 cm2