please answer this question friends it is urgent
Answers
Answer:
ANSWER
We know that, tangent of a circle is perpendicular to the radius of the circle through the point of contact.
⇒ ∠OAP=90
o
⇒ cosθ=
OP
OA
⇒ cosθ=
10
5
⇒ cosθ=
2
1
⇒ θ=cos
−1
(
2
1
)
∴ θ=60
o
⇒ ∠AOB=60
o
+60
o
=120
o
⇒ Reflex ∠AOB=360
o
−∠AOB
=∠360
o
−120
o
=240
o
∴ α=240
o
We know that,Length of belt in contact with pulley =ADB
⇒ Length of major arc =
360
o
α
×2π×r
=
360
o
240
o
×2×3.14×5
=
3
62.8
=20.93cm
Now, in right angled triangle OAP we have:
sin60
o
=
OP
AP
2
3
=
10
AP
⇒ AP=5
3
cm
⇒ Area of triangle =
2
1
×Base×Height
=
2
1
×AP×OA
=
2
1
×5
3
×5
=
2
25
5
cm
2
∴ Area of triangle OAP= Area of triangle OBP=
2
25
3
cm
2
⇒ Area of minor sector OACB=
360
o
θ
×πr
2
=
360
o
120
o
×3.14×5×5
=
3
78.5
Answer:
gffgijbccclifcxxx vjixshjvxgib