If in a $\triangle ABC$,$AD$,$BE$,and $CF$ are the altitudes and $R$ is the circumradius of $\triangle ABC$,then the radius of the circumcircle of $\triangle DEF$ is

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

In $\triangle ABC$,suppose the exradii opposite to angles $A, B$ and $C$ are denoted by $r_1, r_2$ and $r_3$ respectively. If $r_1=2, r_2=3, r_3=6$ and $R$ is the radius of the circumcircle,then the value of $r_1+r_2+r_3-r$ is:

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

In a right $\triangle ABC$,the incircle touches the hypotenuse $AC$ at $D$. If $AD=10$ and $DC=3$,the inradius of $\triangle ABC$ is

Let $ABC$ be an equilateral triangle with side length $a$. Let $R$ and $r$ denote the radii of the circumcircle and the incircle of triangle $ABC$ respectively. Then,as a function of $a$,the ratio $\frac{R}{r}$