The radius of the incircle of a triangle $PQR$ with vertices $P(0, 0)$,$Q(3, 0)$,and $R(0, 4)$ is:

In a $\Delta ABC$, if $\angle C = 90^{\circ}$, $r$ and $R$ are the inradius and circumradius of the $\Delta ABC$ respectively, then $2(r+R)$ is equal to

In a $\triangle ABC$,which of the following formulae are correct?
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$

If $\alpha, \beta, \gamma$ are the lengths of the tangents from the vertices of a triangle to its incircle,then:

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 $\Delta ABC,$ 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 ....... .