Three equal circles each of radius 1 cm are circumscribed by a larger circle. Find the perimeter of the circumscribing circle.

AB = BC = CA = 2 cm.

BD = CD = 1 cm

$\mathrm{AD}=\sqrt{2^{2}-1^{2}}=\sqrt{4-1}=\sqrt{3} \mathrm{~cm}$

$\mathrm{OD}=\frac{1}{3} \mathrm{AD}=\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}} \mathrm{~cm} .$

$\therefore \mathrm{OB}=\sqrt{1^{2}+\frac{1}{3}}=\sqrt{\frac{3+1}{3}}=\frac{2}{\sqrt{3}} \mathrm{~cm} .$

$\therefore \mathrm{OE}=$ Circum-radius

$=\mathrm{OB}+\mathrm{BE}=\frac{2}{\sqrt{3}}+1=\frac{2+\sqrt{3}}{\sqrt{3}} \mathrm{~cm}$

$\therefore$ Required perimeter

$=2 \pi \mathrm{r}=2 \pi\left(\frac{2+\sqrt{3}}{3}\right) \mathrm{cm} \text {. }$