Question

In the adjoining figure, the radius of the inner circle, if other circles are of radii $1$m, is

• A. $(\sqrt{2}-1)m$
• B. $\sqrt{2}m$
• C. $\frac{1}{\sqrt{2}}m$
• D. $\frac{2}{\sqrt{2}}m$

Answer 1

The correct option is A $(\sqrt{2}-1)m$

In $\Delta ABC,{AB}^2+{BC}^2={AC}^2$

$\Rightarrow AC=\sqrt{2^2+2^2}=2\sqrt{2}m$

Now, AC = $1+d+1$

$\Rightarrow 2\sqrt{2}=2+d$

$\Rightarrow 2(\sqrt{2}-1)=d$

$\therefore$ Radius of inner circle $=$ $\frac{d}{2}=\frac{2(\sqrt{2}-1)}{2}=\sqrt{2}-1m$