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Which of the following expresses the cir...

Which of the following expresses the circumference of a circle inscribed in a sector `O A B` with radius `Ra n dA B=2a ?` (a)`2pi(R a)/(R+a)` (b) `(2piR^2)/a` `(c) 2pi(r-a)^2` (d) `2piR/(R-a)`

A

`2pi (Ra)/(R + a)`

B

`(2pi R^(2))/(a)`

C

`2pi (R -a)^(2)`

D

`2pi(R)/(R -a)`

Text Solution

Verified by Experts

The correct Answer is:
A
Triangles OqM and ONA are similar
`rArr (r)/(a) = (R-r)/(R)`
`rArr (r)/(a) = 1 - (r)/(R)`
`rArr (r)/(a) + (r)/(R) =1`
`rArr (r(R+a))/(Ra) = 1`
`rArr r = (Ra)/(R+a)`
`:.` Circumference `= 2pi (Ra)/(R+a)`
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