Mathematics - Properties of Triangle Question with Solution | TestHub

$\frac{\mathrm{r}}{{\mathrm{r}}_1}=\tan \frac{\mathrm{B}}{2}\tan \frac{\mathrm{C}}{2}=\frac{1}{2}$

$$\begin{array}{rlr}& \tan \frac{\mathrm{A}}{2}\left(\tan \frac{\mathrm{B}}{2}+\tan \frac{\mathrm{C}}{2}\right)=1-\tan \frac{\mathrm{B}}{2}\tan \frac{\mathrm{C}}{2}=\frac{1}{2}& \therefore 4\tan \frac{\mathrm{A}}{2}\left(\tan \frac{\mathrm{B}}{2}+\tan \frac{\mathrm{C}}{2}\right)=2\end{array}$$