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)`

Explanation

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`

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