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

The length of the altitude through $A$ of the triangle $ABC$,where $A \equiv (-3, 0)$,$B \equiv (4, -1)$,and $C \equiv (5, 2)$,is

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

$A$ square of side length $a$ has one vertex at the origin and one side along the $x$-axis. The side passing through the origin makes an angle $\alpha$ $(0 < \alpha < \pi/4)$ with the positive $x$-axis. Find the equation of the diagonal that does not pass through the origin.

If $P(\sin \alpha, \cos \alpha)$ lies inside the triangle formed by the vertices $(0,0), \left(\frac{\sqrt{3}}{2}, 0\right)$ and $\left(0, \frac{\sqrt{3}}{2}\right)$,then $\alpha$ lies in the interval

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