The points $(0, -1), (2, 1), (0, 3),$ and $(-2, 1)$ are the vertices of which figure?

If the points $(a, b)$,$(a', b')$ and $(a - a', b - b')$ are collinear,then:

The circumradius of the triangle formed by the lines $xy+2x+2y+4=0$ and $x+y+2=0$ is

Let $ABC$ be an equilateral triangle,and let $KLMN$ be a rectangle with $K, L$ on $BC$,$M$ on $AC$,and $N$ on $AB$. Suppose $AN / NB = 2$ and the area of $\triangle BKN$ is $6$. The area of the $\triangle ABC$ is:

Suppose $ABOC$ is a rhombus in the first quadrant with $O$ being the origin. If the vertices $B$ and $C$ of $\triangle ABC$ lie respectively on $y=\frac{4}{3}x$ and $y=0$,and the side $BC$ passes through $\left(\frac{2}{3}, \frac{2}{3}\right)$,then the mid-point of $BC$ is

If the incentre of the triangle formed by the lines $x-2=0$,$x+y-1=0$,and $x-y+3=0$ is $(\alpha, \beta)$,then $\beta=$