Find the radius of a circle that touches the $y-$axis at point $P(0,2)$ and touches the circle $x^2 + y^2 = 16$ internally.

If the radical axis of the circles $x^2 + y^2 - 1 = 0$ and $x^2 + y^2 - 2x - 2y + 1 = 0$ forms a triangle of area $A$ with the coordinate axes,then the value of $\frac{1}{A}$ is

If the points $(2, 0), (0, 1), (4, 5)$ and $(0, c)$ are concyclic,then $c$ is equal to

Let $O$ be the centre of the circle $x^2 + y^2 = r^2$,where $r > \frac{\sqrt{5}}{2}$. Suppose $PQ$ is a chord of this circle and the equation of the line passing through $P$ and $Q$ is $2x + 4y = 5$. If the centre of the circumcircle of the triangle $OPQ$ lies on the line $x + 2y = 4$,then the value of $r$ is:

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b=$

If the circle $(x - h)^2 + (y - k)^2 = r^2$ touches the curve $y = x^2 + 1$ at the point $(1, 2)$,then the possible locations of the points $(h, k)$ are given by