When will the line $y = x + c$ intersect the circle $x^2 + y^2 = 1$ at two coincident points?

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

If the tangents drawn at the points $O(0,0)$ and $P(1+\sqrt{5}, 2)$ on the circle $x^{2}+y^{2}-2x-4y=0$ intersect at the point $Q$,then the area of the triangle $OPQ$ is equal to

If the line $y=2x+c$ is a tangent to the circle $x^2+y^2=5$,then a value of $c$ is

$A$ triangle is formed by the tangents at the point $(2,2)$ on the curves $y^2=2x$ and $x^2+y^2=4x$,and the line $x+y+2=0$. If $r$ is the radius of its circumcircle,then $r^2$ is equal to $........$.

If the straight line $y = mx + c$ touches the circle ${x^2} + {y^2} - 4y = 0$,then the value of $c$ will be