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

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

$ABC$ is an isosceles triangle with an inscribed circle with center $O$. Let $P$ be the midpoint of $BC$. If $AB = AC = 15$ and $BC = 10$,then $OP$ equals

In $\Delta ABC$,$AB = AC$. Let $P_1$ denote the incircle of $\Delta ABC$. Circle $P_2$ is tangent to sides $AB$,$AC$ and to circle $P_1$. If the radii of circles $P_1$ and $P_2$ are $2$ and $1$ respectively,then the area of $\Delta ABC$ is:

In $\triangle ABC$,if $a: b: c = 4: 5: 6$,then the ratio between the circumradius and the inradius is

In an equilateral triangle,the inradius $(r)$ and the circumradius $(R)$ are connected by which of the following relations?