$A$ pair of straight lines $x^2 - 8x + 12 = 0$ and $y^2 - 14y + 45 = 0$ form a square. The coordinates of the centre of the circle inscribed in the square are

One of the vertices of a square is the origin,and the adjacent sides of the square lie along the positive $x$ and $y$ axes. If the side length is $5$,which of the following is $NOT$ a vertex of the square?

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

Three vertices of a triangle are $A(4, 3)$,$B(1, -1)$,and $C(7, k)$. The value$(s)$ of $k$ for which the centroid,orthocentre,incentre,and circumcentre of the $\Delta ABC$ lie on the same straight line is/are:

If two opposite vertices of a square are $(5, -4)$ and $(-3, 2)$,find its area.

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 $^{\circ}$)