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

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 $\frac{R}{r}$

In triangle $ABC$,if $a=6, b=8$ and $c=10$,then $\frac{2 r_2 r_3}{r r_1} = $

In $\triangle ABC$,if $b=2, c=\sqrt{3}$,and $A=30^{\circ}$,then its inradius $r=$

In an equilateral triangle,the inradius $(r)$ and the circumradius $(R)$ are connected by which of the following relations?

Let $ABC$ be a scalene triangle with incentre $I$ and circumcentre $O$. Suppose $B, C, I, O$ are concyclic points. Then $\angle B + \angle C$ is (in $^{\circ}$)