SSC CGL 9 Aug 2015 Shift 2 Paper

OO' = ${\mathit{r}}_1+{\mathit{r}}_2$ = 14 cm. --(i)
Again $\mathit{\pi }{\mathit{r}}_1^2+\mathit{\pi }{\mathit{r}}_2^2$ = 130π
⇒ ${\mathit{r}}_1^2+{\mathit{r}}_2^2$ = 130
⇒ ${\mathit{r}}_1^2$ + ${\left(14-{\mathit{r}}_2\right)}^2$ = 130
[From equation (i)]
⇒ ${\mathit{r}}_1^2$ + 196 - 28 ${\mathit{r}}_1+{\mathit{r}}_2^2$ = 130
⇒ $2{\mathit{r}}_1^2$ - 28 ${\mathit{r}}_1$ + 196 - 130 = 0
⇒ $2{\mathit{r}}_1^2-28{\mathit{r}}_1$ + 66 = 0
⇒ ${\mathit{r}}_1^2-14{\mathit{r}}_1$ + 33 = 0
⇒ ${\mathit{r}}_1^2-11{\mathit{r}}_1-3{\mathit{r}}_1$ + 33 = 0
⇒ ${\mathit{r}}_1$ (${\mathit{r}}_1$ - 11) - 3 (${\mathit{r}}_1$ - 11) = 0
⇒ (${\mathit{r}}_1$ - 11) (${\mathit{r}}_1$ - 3) = 0
⇒ ${\mathit{r}}_1$ = 11 or 3 cm
∴ ${\mathit{r}}_2$ = 3 or 11 cm