Question

Three equal circles of radius 1 cm touches each other. What is smallest radius of circle touching all three.

Answer 1

The simple formula :-
$\frac{1}{\sqrt{C}}=\frac{1}{\sqrt{a}}\times \frac{1}{\sqrt{b}}$, where a & b are radius of largest circles and c, is radius of smallest circles.
$\therefore \frac{1}{\sqrt{C}}=\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{1}}=2$
$\Rightarrow \sqrt{C}=\frac{1}{2}\Rightarrow C=\frac{1}{4}$