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

Two tangents drawn from $P(1, 7)$ to the circle $x^2 + y^2 = 25$ touch the circle at $Q$ and $R$ respectively. The area of the quadrilateral $PQOR$ is

Let $A$ be the centre of the circle $x^2+y^2-2x-4y-20=0$. If the tangents drawn at the points $B(1,7)$ and $D(4,-2)$ on the given circle meet at the point $C$,then the area of the quadrilateral $ABCD$ is

If the tangent at the point $P$ on the circle $x^2+y^2+6x+6y=2$ meets the straight line $5x-2y+6=0$ at a point $Q$ on the $Y$-axis,then the length of $PQ$ is

If the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle,then its radius is

The equation of the tangent to the circle $x^2 + y^2 - 22x - 4y + 25 = 0$ which is perpendicular to the line $5x + 12y + 8 = 0$ is: