The angle between the tangents drawn from the origin $(0, 0)$ to the circle $(x - 7)^2 + (y + 1)^2 = 25$ is (in $^\circ$)

The equation of the normal to the circle $x^2+y^2=16$ at the point $\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$ is

Let $ABCD$ be a square of side length $1$. $A$ circle $C_{1}$ centered at $A$ with unit radius is drawn. Another circle $C_{2}$ which touches $C_{1}$ and is tangent to the lines $AD$ and $AB$ is also drawn. Let a tangent line from the point $C$ to the circle $C_{2}$ meet the side $AB$ at $E$. If the length of $EB$ is $\alpha+\sqrt{3} \beta,$ where $\alpha, \beta$ are integers,then $\alpha+\beta$ is equal to.........

The length of the tangent from $(6,8)$ to the circle $x^2+y^2=4$ is

If $x-2y=0$ is a tangent drawn at a point $P$ on the circle $x^2+y^2-6x+2y+c=0$,then the distance of the point $(6,3)$ from $P$ is

For what possible value of $p$ is the line $x \cos \alpha + y \sin \alpha = p$ a tangent to the circle $x^2 + y^2 - 2qx \cos \alpha - 2qy \sin \alpha = 0$?