Let $n \geq 3$ be an integer. Assume that inside a big circle, exactly $n$ small circles of radius $r$ can be drawn so that each small circle touches the big circle and also touches both its adjacent small circles. Then, the radius of the big circle is\\
(A) $r \operatorname{cosec} \frac{\pi}{n}$\\
(B) $r \left( 1 + \operatorname{cosec} \frac{2\pi}{n} \right)$\\
(C) $r \left( 1 + \operatorname{cosec} \frac{\pi}{2n} \right)$\\
(D) $r \left( 1 + \operatorname{cosec} \frac{\pi}{n} \right)$