In $\triangle ABC$,if $a=13 \text{ cm}, b=14 \text{ cm}$ and $c=15 \text{ cm}$,then its circumradius $R$ is:

In $\Delta ABC,$ if $b = 6, c = 8$ and $\angle A = 90^\circ,$ then the circumradius $R$ is:

In $\triangle ABC$,if $b=2, c=\sqrt{3}$,and $A=30^{\circ}$,then its inradius $r=$

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 a $\triangle ABC$,if $a=13, b=14, c=15$,then find the value of $r_1$.

In a $\triangle ABC$, $\frac{\Delta^2}{a^2+b^2+c^2}\left(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}\right) = $