If $I$ is the incentre of $\triangle ABC$ and $P_1, P_2, P_3$ are respectively the radii of the circumcircles of the $\triangle IBC, \triangle ICA$ and $\triangle IAB$,then $P_1 P_2 P_3=$

In $\triangle ABC$,if $r_1=3, r_2=10$ and $r_3=15$,then $R=$

In a triangle $ABC$,if $r_1=3, r_2=4, r_3=6$,then $b=$

In $\triangle ABC$,if $a=8, b=10, c=12$,then $\frac{r}{R}=$

The sides of a right-angled triangle are integers. The length of one of the sides is $12$. The largest possible radius of the incircle of such a triangle is

In a $\triangle ABC$, $r_1, r_2$ and $r_3$ respectively denote the radii of the excircles opposite to the vertices $A, B, C$ and $r$ denotes the radius of the incircle. If $p_1, p_2$ and $p_3$ respectively are the altitudes of the triangle from the vertices $A, B$ and $C$, then $\left(\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}\right)^2$ is equal to