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

If $d_1, d_2, d_3$ are the diameters of three ex-circles of a $\triangle ABC$,then $d_1 d_2 + d_2 d_3 + d_3 d_1 =$

Let $A$ be the area of the in-circle and $A_1, A_2, A_3$ be the areas of the ex-circles of a triangle. If $A_1=4, A_2=9, A_3=16$, then $A=$

In $\Delta ABC,$ the lengths of sides $AC$ and $AB$ are $12 \, cm$ and $5 \, cm,$ respectively. If the area of $\Delta ABC$ is $30 \, cm^{2}$ and $R$ and $r$ are respectively the radii of the circumcircle and incircle of $\Delta ABC,$ then the value of $2R + r$ (in $cm$) is equal to ....... .

$\frac{1}{r^2}+\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}$ equals

In an equilateral triangle $ABC$, the ratio $r : R : r_1$ is