If the angle of intersection at a point where the two circles with radii $5 \ cm$ and $12 \ cm$ intersect is $90^o$,then the length (in $cm$) of their 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 the tangent to the circle $x^2+y^2-4x+2y-5=0$ at $(3,-4)$ cuts the circle $x^2+y^2+16x+2y+10=0$ at $A$ and $B$,then the midpoint of $AB$ is:

Given that $a > 2b > 0$ and that the line $y = mx - b \sqrt{1 + m^2}$ is a common tangent to the circles $x^2 + y^2 = b^2$ and $(x - a)^2 + y^2 = b^2$. Then the positive value of $m$ is

If tangents are drawn from the point $(5, -3)$ to the circle $x^2 + y^2 = 10$,then the equation of the chord of contact is:

If the chord of contact of tangents from a point $A$ to a given circle passes through $B$,then the circle with $AB$ as a diameter will . . . . . .