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Three circles of same radius r are drawn such that they touches each other externally. The radius of the circle which touches all the three circles is

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a

$(2 + \sqrt{2}) \frac{r}{\sqrt{3}}$

b

$(2 - \sqrt{3}) \frac{r}{\sqrt{3}}$

c

$(3 + 2 \sqrt{3}) \frac{r}{3}$

d

$(2 - \sqrt{2}) \frac{r}{\sqrt{3}}$

answer is A, B.

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Detailed Solution

Question Image

Let ris radius of small circle, $r_{1}$ be radius of bigger circle
In Triangle $△ ACB$
$\cos 120^{0} = \frac{{(r + r_{1})}^{2} + {(r + r_{1})}^{2} - 4 r^{2}}{2 (r + r_{1}) (r + r_{1})} B y s i m p l i f i c a t i o n w e g e t r_{1} = (2 \pm \sqrt{3}) \frac{r}{\sqrt{3}}$

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