Let $A B$ be a chord of length $12$ of the circle $(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$ If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$, then five times the distance of point $P$ from chord $AB$ is equal to$.......$

If the line $y = mx + c$be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then the point of contact is

The equation of the tangent to the circle ${x^2} + {y^2} = {r^2}$ at $(a,b)$ is $ax + by - \lambda = 0$, where $\lambda $ is

Let the tangents drawn from the origin to the circle, $x^{2}+y^{2}-8 x-4 y+16=0$ touch it at the points $A$ and $B .$ The $(A B)^{2}$ is equal to

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2 + y^2 + 4x -6y = 12$ externally at the point $(1, -1)$, then the radius of $C$ is

Let the tangents at the points $A (4,-11)$ and $B (8,-5)$ on the circle $x^2+y^2-3 x+10 y-15=0$, intersect at the point $C$. Then the radius of the circle, whose centre is $C$ and the line joining $A$ and $B$ is its tangent, is equal to