The area of the triangle bounded by the straight line $ax + by + c = 0$ $(a, b, c \neq 0)$ and the coordinate axes is

If the points of intersection of the coordinate axes and $|x+y|=2$ form a rhombus,then its area is

If a pair of perpendicular lines through the origin together with the straight line $2x + 3y = 6$ form an isosceles triangle,then the area of that triangle (in sq units) is

Let $ABC$ be a triangle with $A(-3, 1)$ and $\angle ACB = \theta$,where $0 < \theta < \frac{\pi}{2}$. If the equation of the median through $B$ is $2x + y - 3 = 0$ and the equation of the angle bisector of $C$ is $7x - 4y - 1 = 0$,then $\tan \theta$ is equal to:

If the incentre of the triangle formed by the lines $x-2=0$,$x+y-1=0$,and $x-y+3=0$ is $(\alpha, \beta)$,then $\beta=$

If $P(\sin \alpha, \cos \alpha)$ lies inside the triangle formed by the vertices $(0,0), \left(\frac{\sqrt{3}}{2}, 0\right)$ and $\left(0, \frac{\sqrt{3}}{2}\right)$,then $\alpha$ lies in the interval