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) $r \left( 1 + \operatorname { cosec } \frac { \pi } { 2 n } \right)$ (D) $r \left( 1 + \operatorname { cosec } \frac { \pi } { n } \right)$
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) $r \left( 1 + \operatorname { cosec } \frac { \pi } { 2 n } \right)$\\
(D) $r \left( 1 + \operatorname { cosec } \frac { \pi } { n } \right)$