If inside a big circle exactly `n(nlt=3)` small circles, each of radius `r ,` can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then the radius of big circle is `r(1+cos e cpi/n)` (b) `((1+tanpi/n)/(cospi/pi))` `r[1+cos e c(2pi)/n]` (d) `(r[sin pi/(2n)+cospi/(2n)]^2)/(sinpi/n)`

Options

A. `r(1 + cosec.(pi)/(n))`
B. `((1 + tan pi//n)/(cos pi//n))`
C. `r[1 + cosec.(2pi)/(n)]`
D. `(r[sin.(pi)/(2n) + cos.(2pi)/(n)]^(2))/(sin pi//n)`

Answer

A, D

Explanation

If R is radius of bigger circle, then `sin ((pi)/(n)) = (r)/(R-r)`
or `R = r (1 + cosec((pi)/(n))) =(r["sin"(pi)/(2n) + "cos"(pi)/(2n)]^(2))/("sin"(pi)/(n))`