The radius of the circle whose arc of length $15 \ cm$ makes an angle of $3/4$ radian at the centre is ..... $cm$.

The inverse point of $(1, 3)$ with respect to the circle $x^2 + y^2 - 4x - 6y + 9 = 0$ is

In a rectangle $ABCD$,the coordinates of $A$ and $B$ are $(1, 2)$ and $(3, 6)$ respectively,and some diameter of the circumscribing circle of $ABCD$ has the equation $2x - y + 4 = 0$. Then,the area of the rectangle is

The equation of the circle which touches the circle $S \equiv x^2+y^2-10x-4y+19=0$ at the point $(2,3)$ internally and has a radius equal to half of the radius of the circle $S=0$ is:

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

If $(3,-2)$ is the centre of the circle $S \equiv x^2+y^2+2gx+2fy-23=0$ and $A$ is a point on the circle $S=0$ such that its distance from a point $P(-1,-5)$ is least,then $A=$