Find the distance from the center of the circle $x^2 + y^2 = 2x$ to the common chord of the circles $x^2 + y^2 + 5x - 8y + 1 = 0$ and $x^2 + y^2 - 3x + 7y - 25 = 0$.

$A$ pair of tangents is drawn from every point on the line $3x + 4y = 12$ to the circle $x^2 + y^2 = 4$. Their variable chord of contact always passes through a fixed point whose coordinates are:

$A$ circle $C_1$ of unit radius lies in the first quadrant and touches both coordinate axes. The radius of another circle that touches both coordinate axes and intersects $C_1$ such that the common chord is of maximum length is:

The radius of the circle whose diameter is the common chord of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2+4x+3y+2=0$ is

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

The equation of the pair of tangents at $(0,1)$ to the circle $x^{2}+y^{2}-2x-6y+6=0$ is