Two sides of a parallelogram are along the lines $4x + 5y = 0$ and $7x + 2y = 0$. If the equation of one of the diagonals of the parallelogram is $11x + 7y = 9$,then the other diagonal passes through the point:

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:

Six consecutive sides of an equiangular octagon are $6, 9, 8, 7, 10, 5$ in that order. The integer nearest to the sum of the remaining two sides is

Let $ABCD$ be a quadrilateral such that there exists a point $E$ inside the quadrilateral satisfying $AE=BE=CE=DE$. Suppose $\angle DAB, \angle ABC, \angle BCD$ are in an arithmetic progression. Then the median of the set $\{\angle DAB, \angle ABC, \angle BCD\}$ is

In a $\triangle ABC$,$2x+3y+1=0$ and $x+2y-12=0$ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively. If $A$ is $(3,2)$,then the slope of the side $BC$ is

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