The length of the chord intercepted by the circle $x^2+y^2-8x-2y-8=0$ on the line $x+y+1=0$ is:

If the diameter of the circle $2(x^2 + y^2) + 3x + 4y - 1 = 0$ is $y = 2x + k$,then $k = \dots$

If the equation of the circle whose radius is $\sqrt{10}$ and which touches the circle $x^2+y^2+2x+8y-23=0$ externally at the point $(1,2)$ is $x^2+y^2+ax+by+c=0$,then $|a+b+c|=$

The equation of the circle with $(1,1)$ as centre and which cuts a chord of length $4 \sqrt{2}$ units on the line $x+y+1=0$ is

Let two circles $C_1$ and $C_2$ of radii $r_1 = 2$ and $r_2 = 4$ be tangent to each other at point $P$ and tangent to a common straight line (not passing through $P$) at points $Q$ and $R$ respectively. Then the value of $PQ^2 + QR^2 + RP^2$ is:

The angle between the circles $x^2+y^2+4x-14y+28=0$ and $x^2+y^2-12x-6y-4=0$ is