Radius of Incircle of a Triangle Given its Excircles

If we let the radii of the excircles be $e_{1}$ , $e_{2}$ and $e_{3}$ and then let the radius of the incircle be ${r}$ . There is a formula which states that: $\frac{1}{e_1}\ + \frac{1}{e_2}\ + \frac{1}{e_3}\ = \frac{1}{r}\Rightarrow\frac{1}{r}\ = \frac{6+3+2}{66}\ = \frac{1}{6}\therefore\ r= 6$