Area of the circle in which a chord of length $\sqrt{2}$ makes an angle $\frac{\pi}{2}$ at the centre is

The length of the chord intercepted by the circle $x^2+y^2+2x+4y-20=0$ on the line $3x+4y-6=0$ is

The number of common tangents to the circles $x^2+y^2-18x-15y+131=0$ and $x^2+y^2-6x-6y-7=0$ is:

If one end of a diameter of the circle $3x^{2}+3y^{2}-9x+6y+5=0$ is $(1,2)$, then the other end is

If two circles $(x - 1)^2 + (y - 3)^2 = r^2$ and $x^2 + y^2 - 8x + 2y + 8 = 0$ intersect in two distinct points,then

$A$ square is inscribed in the circle $x^2 + y^2 - 6x + 8y - 103 = 0$ with its sides parallel to the coordinate axes. Then the distance of the vertex of the square which is nearest to the origin is