1.

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

Answer» We can create a diagram with the given details.
Please refer to video for the diagram.
From the diagram,
`sintheta = r/(OM) = a/(AO)`
`=>r/a = (OM)/R`
`=>r/a = (R-r)/R`
`=>r/a = 1 - r/R`
`=>r/a+r/R = 1`
`=>r((a+R)/(aR) ) = 1`
`=> r = (aR)/(a+R)`
`:.` Circumference ` = 2pir = 2pi ((aR)/(a+R))`
So, option `(a)` is the correct option.


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