The circles $x^2 + y^2 - 10x + 16 = 0$ and $x^2 + y^2 = r^2$ intersect each other in two distinct points,if

The shortest distance from the line $3x + 4y = 25$ to the circle $x^2 + y^2 - 6x + 8y = 0$ is

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 ............ $^o$.

The sum of the minimum and maximum distance of the point $(4, -3)$ to the circle $x^2 + y^2 + 4x - 10y - 7 = 0$ is:

Given $r_1, r_2 > 0$ and $C_1, C_2$ are the centres of two circles having only two common tangents. If $C_1 C_2 = r_1 + r_2$,which of the following is correct?

The least distance of the point $A(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is the length of segment $AM$. If $MM'$ is the diameter of the circle,then the lengths of $AM$ and $AM'$ are respectively . . . . . . , . . . . . . units.