If the equations of three sides of a triangle are $x = 2$,$y + 1 = 0$,and $x + 2y = 4$,then the coordinates of the circumcentre of this triangle are:

$A$ farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as $4 \text{ cm}$,$5 \text{ cm}$,and $7 \text{ cm}$. Then the area of land of the farmer in $\text{sq. cm}$ is

$x+8y-22=0$, $5x+2y-34=0$, and $2x-3y+13=0$ are the three sides of a triangle. The area of the triangle is

Let $O$ denote the origin. If $M(1, 2)$,$N(0, 1)$,and $A(x, y)$ are points such that $xy > 0$ and $x + y < 1$,then choose the correct statement.

The coordinates of three points $A(-4, 0)$,$B(2, 1)$,and $C(3, 1)$ determine the vertices of an isosceles trapezium $ABCD$. The coordinates of the vertex $D$ are:

Let $ABC$ be an isosceles triangle in which $A$ is at $(-1, 0)$,$\angle A = \frac{2\pi}{3}$,$AB = AC$ and $B$ is on the positive $x$-axis. If $BC = 4\sqrt{3}$ and the line $BC$ intersects the line $y = x + 3$ at $(\alpha, \beta)$,then $\frac{\beta^4}{\alpha^2}$ is :