In $\triangle A B C, \sqrt{\frac{r \cdot r_2}{r_3 r_1}}=$

If $A(0,0,0) B(3,4,0)$ and $C(0,12,5)$ are the vertices of a $\triangle A B C$, then the $x$-coordinate of its incentre is

In a $\triangle A B C$, if $\sin \frac{A}{2}=\frac{1}{4} \sqrt{\frac{3}{5}}, a=2, c=5$ and $b$ is an integer, then the area (in sq. units) of $\triangle A B C$ is

In a $\triangle A B C$ if $a+c=5 b$, then $\cot \frac{A}{2} \cot \frac{C}{2}=$