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) $r \left( 1 + \operatorname { cosec } \frac { \pi } { n } \right)$.
(d) Let $s$ be distance between the centre of the big circle and the centre of (any) one of the small circles. Then there exists a right angle triangle with hypotenuse $s$, side $r$ and angle $\frac { \pi } { n }$.
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) $r \left( 1 + \operatorname { cosec } \frac { \pi } { n } \right)$.