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 $A(1,2)$ and $B(2,1)$ are two vertices of an acute-angled triangle and $S(0,0)$ is its circumcentre,then the angle subtended by $AB$ at the third vertex is

If the circles $x^2+y^2+2hx+2ky=0$ and $x^2+y^2+2h'x+2k'y=0$ touch each other,then $\frac{h'k}{hk'} = $

Let $S$ be the circle in the $XY$-plane which touches the $X$-axis at point $A$,the $Y$-axis at point $B$,and the unit circle $x^2+y^2=1$ at point $C$ externally. If $O$ denotes the origin,then the angle $\angle OCA$ equals:

Let $ABCD$ be a quadrilateral with area $18$,with side $AB$ parallel to the side $CD$ and $AB = 2CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides,then its radius is

Consider the circles $x^2 + (y - 1)^2 = 9$ and $(x - 1)^2 + y^2 = 25$. Which of the following is true?