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:

The equation of the circle having the common chord of the circles $x^2+y^2-8x=0$ and $x^2+y^2-9=0$ as its diameter is

If $P$ and $Q$ are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$,then there is a circle passing through $P, Q$ and $(1, 1)$ for:

The length of the common chord of the circles $x^2+y^2-6x+5=0$ and $x^2+y^2+4y-5=0$ 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

The length of the common chord of the circles $(x - a)^2 + y^2 = a^2$ and $x^2 + (y - b)^2 = b^2$ is