If vertices of a parallelogram are respectively $(0, 0)$, $(1, 0)$, $(2, 2)$ and $(1, 2)$, then angle between diagonals is 

Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is $3x + 4y = 4$ and the opposite vertex of the hypotenuse is $(2, 2)$, will be

In an isosceles triangle $ABC, \angle C = \angle A$ if point of intersection of bisectors of internal angles $\angle A$ and $\angle C$ divide median of side $AC$ in $3 : 1$ (from vertex $B$ to side $AC$), then value of $cosec \ \frac{B}{2}$ is equal to

A square of side a lies above the $x$ -axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha ,(0 < \alpha < \frac{\pi }{4})$ with the positive direction of $x$-axis. The equation of its diagonal not passing through the origin is

The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. unit. The locus of the point is

The sides $AB,BC,CD$ and $DA$ of a quadrilateral are $x + 2y = 3,\,x = 1,$ $x - 3y = 4,\,$ $\,5x + y + 12 = 0$ respectively. The angle between diagonals $AC$ and $BD$ is ......$^o$