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 $^{\circ}$)

In $\triangle ABC$,the expression $\frac{16 R s \Delta \sin \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}}{s-c}$ is equal to

In $\triangle ABC$,with usual notation,observe the two statements given below :
$(I)$ $r r_1 r_2 r_3 = \Delta^2$
$(II)$ $r_1 r_2 + r_2 r_3 + r_3 r_1 = s^2$
Which of the following is correct?

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

The difference between the areas of the circumcircle and the incircle of a regular decagon of side $2 \, cm$ is -

If $a, b$ and $c$ are the sides of $\triangle ABC$ for which $r_1=8, r_2=12$ and $r_3=24$,then the ordered triad $(a, b, c)=$