In $\triangle ABC$, find the value of $r_1+r_2+r_3$.

In a $\triangle ABC$,$D, E$,and $F$ are the points of contact of the incircle with the sides $AB, BC$,and $CA$ respectively,such that $AD=\alpha, BE=\beta$,and $CF=\gamma$. Then $\frac{\alpha \beta \gamma}{\alpha+\beta+\gamma} = $

In a triangle $ABC$, $a=5$, $b=4$ and $\tan \frac{C}{2}=\sqrt{\frac{7}{9}}$, then its inradius $r=$

If $r$ is the inradius,$\Delta$ is the area of $\triangle ABC$,and $s$ is the semi-perimeter,then which of the following is true?

In $\triangle ABC$,find the value of $\frac{r_1-r}{a}+\frac{r_2-r}{b}$.

In $\triangle ABC$,the expression $\frac{16 R s \Delta \sin \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}}{s-c}$ is equal to