Let $ABCD$ be a convex quadrilateral in which $AC = BD$,$AB = CD$,$\angle BAC = 70^{\circ}$ and $\angle BCD = 60^{\circ}$. The acute angle between $AC$ and $BD$ is (in $^{\circ}$)

The area of the parallelogram formed by the lines $y = mx, y = mx + 1, y = nx, y = nx + 1$ is:

The perimeter of a triangle is $16 \text{ cm}$, one of the sides is of length $6 \text{ cm}$. If the area of the triangle is $12 \text{ cm}^2$, then the triangle is:

Let the area of the triangle with vertices $A(1, \alpha)$,$B(\alpha, 0)$,and $C(0, \alpha)$ be $4 \text{ sq. units}$. If the points $(\alpha, -\alpha)$,$(-\alpha, \alpha)$,and $(\alpha^2, \beta)$ are collinear,then $\beta$ is equal to:

The lines $x+y+4=0$,$x-2y-4=0$,and $3x+4y-2=0$:

The circumcentre of the triangle formed by the lines $x = -2$,$y = -2$ and $x + y + 2 = 0$ is