In $\triangle ABC$, if $a=7, b=8$ and $c=9$, then $\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$

In $\triangle ABC$,the expression $\frac{16 R s \Delta \sin \frac{A}{2} \sin \frac{B}{2} \cos \frac{C}{2}}{s-c}$ is equal to

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:

If $\alpha, \beta, \gamma$ are the lengths of the tangents from the vertices of a triangle to its incircle,then:

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 $\Delta ABC$,$AB = AC$. 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: