In an equilateral triangle of side $2\sqrt{3} \text{ cm}$,the circum-radius is ..... $\text{cm}$.

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

In $\triangle ABC$,suppose the radius of the excircle opposite to angle $A$ is denoted by $r_1$,similarly $r_2$ for angle $B$,and $r_3$ for angle $C$. If $r_1=2, r_2=3, r_3=6$,then what is $(a, b, c)$?

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

$ABC$ is a triangle with $\angle A=30^{\circ}$ and $BC=10 \text{ cm}$. The area of the circumcircle of the triangle is

In a triangle $ABC$, if $a:b:c = 4:5:6$, then $\frac{1}{4R}[r_1+r_2+r_3] =$