Find the area of the segment of a circle given the radius of 12 cm and an arc of 90°.
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Answer:
Area of minor segment = Area of sector- Area of ΔOAB
In ΔOAB
Refer image,
θ=60
0
OA=OB=r=12cm
∠B=∠A=x[∠s opp. to equal sides are equal
⇒∠A+∠B+∠O=180
0
⇒x+x+60
0
=180
0
⇒2x=180
0
−60
0
⇒x=
2
120
0
=60
0
∴ΔOAB is equilateral Δ with each side (a)
=12cm
Area of the equilateral Δ=
4
3
a
2
Area of minor segment = Area of the sector - Area of ΔOAB
=
360
0
πr
2
θ
−
4
3
a
2
=
360
0
3.14×12×12×60
0
−
4
3
×12×12
=6.28×12−36
3
Step-by-step explanation:
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