Let $C$ be the circle with centre at $(1, 1)$ and radius $= 1$. If  $T$ is the circle centred at $(0, y),$ passing through origin and touching the circle $C$ externally, then the radius of $T$ is equal 

A circle touches the $y$ -axis at the point $(0,4)$ and passes through the point $(2,0) .$ Which of the following lines is not a tangent to this circle?

Tangents are drawn from any point on the circle $x^2 + y^2 = R^2$ to the circle $x^2 + y^2 = r^2$. If the line joining the points of intersection of these tangents with the first circle also touch the second, then $R$ equals

If $OA$ and $OB$ be the tangents to the circle ${x^2} + {y^2} - 6x - 8y + 21 = 0$ drawn from the origin $O$, then $AB =$

Tangents are drawn from the point $(4, 3)$ to the circle ${x^2} + {y^2} = 9$. The area of the triangle formed by them and the line joining their points of contact is

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of perpendicular from $O$ on $AB$ is