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

If the vertices of a triangle are $(2, -2)$,$(8, -2)$,and $(8, 6)$,what is the excenter opposite to the vertex $(2, -2)$?

If $\triangle ABC$ is right-angled at $A$, then $r_2+r_3$ is equal to

In a triangle $ABC$, with usual notation, if $a=12, b=16, c=20$, then the ratio of the exradii of the triangle opposite to the angles in the order $\angle C, \angle B, \angle A$ is

$AD, BE$ and $CF$ are the perpendiculars from the vertices of a $\Delta ABC$ to the opposite sides. The ratio of the perimeter of $\Delta DEF$ to the perimeter of $\Delta ABC$ is: (where $r$ is the inradius and $R$ is the circumradius of $\Delta ABC$)

In a $\triangle ABC$,if $\frac{2 r_2 r_3}{r_2-r_1}=r_3-r_1$,then $\frac{r_1(r_2+r_3)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} = $