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 $^{\circ}$)

$AD, BE$ 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 $\triangle ABC$,find the value of $\frac{r_1-r}{a}+\frac{r_2-r}{b}$.

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

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

In $\triangle ABC$,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?