In $\triangle ABC$,if $r=1, R=4$ and $\Delta=8$,then $\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=$

$ABC$ 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 a triangle $XYZ$,let $x, y, z$ be the lengths of sides opposite to the angles $X, Y, Z$,respectively,and $2s = x+y+z$. If $\frac{s-x}{4} = \frac{s-y}{3} = \frac{s-z}{2}$ and the area of the incircle of the triangle $XYZ$ is $\frac{8\pi}{3}$,then:

In $\triangle ABC$,if $r_1=3, r_2=10$ and $r_3=15$,then $R=$

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

In a triangle $ABC$, $a=5$, $b=4$ and $\tan \frac{C}{2}=\sqrt{\frac{7}{9}}$, then its inradius $r=$