Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.

Column $I$	Column $II$
$(A)$ Two intersecting circles	$(p)$ have a common tangent
$(B)$ Two mutually external circles	$(q)$ have a common normal
$(C)$ two circles, one strictly inside the other	$(r)$ do not have a common tangent
$(D)$ two branches of a hyperbola	$(s)$ do not have a common normal

The line $2 x - y +1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is

If the line $3x - 4y = \lambda $ touches the circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$, then $\lambda $ is equal to

Let the tangent to the circle $x^{2}+y^{2}=25$ at the point $R (3,4)$ meet $x$ -axis and $y$ -axis at point $P$ and $Q$, respectively. If $r$ is the radius of the circle passing through the origin $O$ and having centre at the incentre of the triangle $OPQ ,$ then $r ^{2}$ is equal to

Pair of tangents are drawn from every point on the line $3x + 4y = 12$ on the circle $x^2 + y^2 = 4$. Their variable chord of contact always passes through a fixed point whose co-ordinates are

In the figure, $A B C D$ is a unit square. A circle is drawn with centre $O$ on the extended line $C D$ and passing through $A$. If the diagonal $A C$ is tangent to the circle, then the area of the shaded region is