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 $\triangle ABC$,the circle that touches the side $BC$ internally and the other two sides $AB$ and $AC$ externally is called:

If the lengths of the sides of a triangle are $15, 20, 25$ units,find the circumradius of the triangle. (in $units$)

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 $ABC$,$(r_2+r_3) \operatorname{cosec}^2\left(\frac{A}{2}\right) =$

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