The number of triangles formed by the lines $x-y+3=0$,$2x-y+3=0$,$3x-y+2=0$,and $x+y-3=0$ is:

If $x_1, x_2, x_3$ and $y_1, y_2, y_3$ are in $G.P.$ with the same common ratio,then the points $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ are:

The incentre of the triangle formed by the lines $x = 0$,$y = 0$,and $3x + 4y = 12$ is

The area of a parallelogram formed by the lines $ax \pm by \pm c = 0$ is

In $\triangle ABC$,let $AD, BE$ and $CF$ be the internal angle bisectors with $D, E$ and $F$ on the sides $BC, CA$ and $AB$ respectively. Suppose $AD, BE$ and $CF$ concur at $I$ and $B, D, I, F$ are concyclic,then $\angle IFD$ has measure $......$

$\Delta ABC$ has integral side lengths. The internal angle bisector of angle $B$ meets side $AC$ at $D$. If $AD = 3$ and $DC = 8$,then the perimeter of $\Delta ABC$ is: