The diagonals of the parallelogram whose sides are $lx + my + n = 0$,$lx + my + n' = 0$,$mx + ly + n = 0$,and $mx + ly + n' = 0$ include an angle of:

Let a point $A$ lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$ are $6$ and $3$ units, respectively. Then the area (in sq. units) of the equilateral triangle $ABC$, where the points $B$ and $C$ lie on the lines $L_1$ and $L_2$ respectively, is:

The equations of two equal sides of an isosceles triangle are $7x - y + 3 = 0$ and $x + y - 3 = 0$. If the third side passes through the point $(1, -10)$,then the equation of the third side is:

If the incentre and the circumcentre of the triangle formed by the lines $x=2$,$4x+3y+7=0$ and $y=3$ are $I$ and $S$ respectively,then $IS=$

The sides of a quadrilateral are all positive integers and three of them are $5, 10, 20$. How many possible values are there for the fourth side?

If the points $(-5, 1), (p, 5)$ and $(10, 7)$ are collinear,then the value of $p$ will be