Q67 / 200 · Manipal (MET) 2014 · Mathematics
A circle of radius 2 is touching both the axes and a circle with centre $(6,5)$. The distance between their centres is
- A8 units
- Correct answerB5 units
- C7 units
- DNone of these
Solution
Radius of smaller circle is $r=2 \mathrm{~cm}$.
Since, it is touching both the axes, so its centre is $(2,2)$.
The distance between their centres $\begin{aligned} & =r+R=\sqrt{(5-2)^2+(6-2)^2} \\ & =\sqrt{3^2+4^2}=\sqrt{25}=5 \text { units } \end{aligned}$
The distance between their centres $\begin{aligned} & =r+R=\sqrt{(5-2)^2+(6-2)^2} \\ & =\sqrt{3^2+4^2}=\sqrt{25}=5 \text { units } \end{aligned}$
Hence, the correct answer is option: 'B'.