The area of the triangle formed by the line $x \sin \alpha + y \cos \alpha = \sin 2\alpha$ and the coordinate axes 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

The equation of one side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is

Two sides of a parallelogram are along the lines $x + y = 3$ and $x - y + 3 = 0$. If its diagonals intersect at $(2, 4)$,then one of its vertices is

The sides of a $\triangle ABC$ are positive integers. The smallest side has length $1$. Which of the following statements is true?

The diagonals $AC$ and $BD$ of a rhombus $ABCD$ intersect at the point $(3,4)$. If $BD=2 \sqrt{2}$,$A=(1,2)$,$B=(\alpha, \beta)$,$D=(\gamma, \delta)$ and $\alpha < \delta < \gamma < \beta$,then $\beta+\gamma-\delta=$