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 $A=$

For a triangle with side lengths $6$,$5$,and $9$,find the inradius of the triangle.

In a $\triangle ABC$,if $r_1=36, r_2=18$ and $r_3=12$,then $s=$

In $\Delta ABC$,$AB = AC$. Let $P_1$ denote the incircle of $\Delta ABC$. Circle $P_2$ is tangent to sides $AB$,$AC$ and to circle $P_1$. If the radii of circles $P_1$ and $P_2$ are $2$ and $1$ respectively,then the area of $\Delta ABC$ is:

Corresponding to a triangle $ABC$,match the items given in List-$I$ with the items given in List-$II$.

List-$I$	List-$II$
$(A)$ $rr_2 = r_1r_3$	$(I)$ $\angle A = 90^{\circ}$
$(B)$ $r_1 + r_2 = r_3 - r$	$(II)$ $b^2 = c^2 + a^2$
$(C)$ $r_1 = r + 2R$	$(III)$ $\angle C = 90^{\circ}$
	$(IV)$ $\angle B = 120^{\circ}$

The correct match is:

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