Two circles centered at $(2,3)$ and $(5,6)$ intersect each other. If the radii are equal,the equation of the common chord is

Let the tangent to the circle $C_{1}: x^{2}+y^{2}=2$ at the point $M(-1, 1)$ intersect the circle $C_{2}: (x-3)^{2}+(y-2)^{2}=5$ at two distinct points $A$ and $B$. If the tangents to $C_{2}$ at the points $A$ and $B$ intersect at $N$,then the area of the triangle $ANB$ is equal to

If tangents are drawn to the circle $x^2+y^2=12$ at the points where it intersects the circle $x^2+y^2-5x+3y-2=0$,then the coordinates of the point of intersection of those tangents are

If $A, B$ are the points of contact of the tangents drawn from the point $P(-2, -3)$ to the circle $x^2+y^2-8x-10y+5=0$ and the chord $AB$ subtends an angle $\theta$ at $P$,then $\tan \theta =$

The common chord of the circles $x^2 + y^2 + 4x + 1 = 0$ and $x^2 + y^2 + 6x + 2y + 3 = 0$ is

The chord of contact of the point $(3, 2)$ with respect to the circle $x^2 + y^2 = 25$ meets the coordinate axes at $A$ and $B$. The circumcentre of triangle $OAB$ is