The value of $c$,for which the line $y = 2x + c$ is a tangent to the circle $x^2 + y^2 = 16$,is

The angle between the tangents to the circle $x^2 + y^2 = 169$ at the points $(5, 12)$ and $(12, -5)$ is ............. $^o$.

If the angle between the pair of tangents drawn to the circle $x^2+y^2-2x+4y+3=0$ from the point $(6,-5)$ is $\theta$,then $\cot \theta=$

$O(0,0)$ and $A(1,0)$ are the centers of two unit circles $C_1$ and $C_2$ respectively. $C_3$ is also a unit circle having its center above the $X$-axis and passing through $O$ and $A$. The equation of the common tangent to $C_1$ and $C_3$ which does not intersect the circle $C_2$ is

Tangents drawn from the origin to the circle $x^2 + y^2 - 2ax - 2by + b^2 = 0$ are perpendicular to each other,if

If $y = c$ is a tangent to the circle $x^2 + y^2 - 2x + 2y - 2 = 0$ at the point $(1, 1)$,then the value of $c$ is: