The angle of intersection of the circles $x^2 + y^2 + 8x - 2y - 9 = 0$ and $x^2 + y^2 - 2x + 8y - 7 = 0$ is ............ $^o$.

Does the point $(-2.5, 3.5)$ lie inside,outside,or on the circle $x^{2}+y^{2}=25$?

The length of the chord intercepted by the circle $x^2+y^2-4x+6y-12=0$ on the line $4x+3y+1=0$ is

If $P(2,3)$ and $Q(-1,2)$ are conjugate points with respect to the circle $x^2+y^2+2gx+3y-2=0$,then the radius of the circle is

Two tangents are drawn from the point $P(-1, 1)$ to the circle $x^{2}+y^{2}-2x-6y+6=0$. If these tangents touch the circle at points $A$ and $B$,and if $D$ is a point on the circle such that the lengths of the segments $AB$ and $AD$ are equal,then the area of the triangle $ABD$ is equal to:

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