Question

Inside the unit circle $S=\left\{\right(x,y)|x^2+y^2=1\}$ there are three smaller circles of equal radius a, touches to each other and also touches to S. The value of a equals?

• A. $\sqrt{2}(\sqrt{2}-1)$
• B. $\sqrt{3}(2-\sqrt{3})$
• C. $\sqrt{2}(2-\sqrt{3})$
• D. $\sqrt{3}(\sqrt{3}-1)$

Answer 1

The correct option is B $\sqrt{3}(2-\sqrt{3})$

$\angle {CC}_{2}O={30}^0$

${CC}_2=(1-a)$

${OC}_2=a$

$\Rightarrow {\cos 30}^0=\frac{a}{1-a}=\frac{\sqrt{3}}{2}$

$\Rightarrow a=\frac{\sqrt{3}}{2+\sqrt{3}}\times \frac{(2-\sqrt{3})}{(2-\sqrt{3})}$

$a=\sqrt{3}(2-\sqrt{3})$