In a triangle $ABC$,if $b = 2$ and $B = 30^\circ$,then the area of the circumcircle of triangle $ABC$ in square units is:

The circumradius of a triangle whose sides are $10 \ units$,$8 \ units$,and $6 \ units$ is (in $units$)

If $\alpha, \beta, \gamma$ are the lengths of the tangents from the vertices of a triangle to its incircle,then:

In a triangle $ABC,$ $a:b:c = 4:5:6$. The ratio of the radius of the circumcircle to that of the incircle is

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

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 $^{\circ}$)