In $\triangle ABC$,if $2R + r = r_2$,then $\angle B$ is equal to

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 ....... .

In a $\triangle ABC$,$a: b: c = 4: 5: 6$. The ratio of the radius of the circumcircle to that of the incircle is

In $\triangle ABC$,the expression $\frac{16 R s \Delta \sin \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}}{s-c}$ is equal to

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