12. The given figure shows a circle with centre O, in which
angke APB = angle CQD. Prove that arc AB = arc CD.
Please give the ans with the diagram..
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Answer:
REF.Image.
Given (
CD
AB
)=
3
5
∠ADB=100
∘
let AB = x
In ΔOAB
cos100
∘
=
2r
2
2r
2
−x
2
cos100
∘
=1−(
2r
x
)
2
(
2r
x
)
2
=1−cos100
∘
2r
2
x
2
=2sin
2
50
∘
x=2rsin50
∘
r = 0.653x
(i) In Δ COD, cos ∠ COD =1−
2r
2
CD
2
cos∠COD=1−
25(2)(0.653)
2
x
2
9x
2
cos∠COD=0.5775
∠COD=54.73
∘
(ii)
CD
ˉ
AB
ˉ
=
(54.73
180
π
)
r
(
180
100π
)(r)
(
CD
ˉ
AB
ˉ
)=1.83
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