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

Options

A. `2pi (Ra)/(R + a)`
B. `(2pi R^(2))/(a)`
C. `2pi (R -a)^(2)`
D. `2pi(R)/(R -a)`

Answer

A

Explanation

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)`