If $R$ is the radius of the circumcircle of the $\Delta ABC$ and $\Delta$ is its area,then

The area of the equilateral triangle which contains three coins of unit radius is

In a $\triangle ABC$, $r_1, r_2$ and $r_3$ respectively denote the radii of the excircles opposite to the vertices $A, B, C$ and $r$ denotes the radius of the incircle. If $p_1, p_2$ and $p_3$ respectively are the altitudes of the triangle from the vertices $A, B$ and $C$, then $\left(\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}\right)^2$ is equal to

The radius of the incircle of a triangle $PQR$ with vertices $P(0, 0)$,$Q(3, 0)$,and $R(0, 4)$ is:

In $\triangle ABC$,suppose the exradii opposite to angles $A, B$ and $C$ are denoted by $r_1, r_2$ and $r_3$ respectively. If $r_1=2, r_2=3, r_3=6$ and $R$ is the radius of the circumcircle,then the value of $r_1+r_2+r_3-r$ is:

In a triangle $ABC$,if $r r_2 = r_1 r_3$,then $\cos 2B =$