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 the sides of a triangle are $3$,$4$,and $5$,then the circumradius of the triangle is

For a triangle with side lengths $6$,$5$,and $9$,find the inradius of the triangle.

If $I$ is the incentre of $\triangle ABC$ and $P_1, P_2, P_3$ are respectively the radii of the circumcircles of the $\triangle IBC, \triangle ICA$ and $\triangle IAB$,then $P_1 P_2 P_3=$

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

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