Which circle among the following bisects the circumference of the circle $x^2+y^2-8x-6y+23=0$?

The equation of the circle passing through the point $(1, 2)$ and through the points of intersection of $x^2 + y^2 - 4x - 6y - 21 = 0$ and $3x + 4y + 5 = 0$ is given by

If the circle passing through $(3,5), (5,5)$ and $(3,-3)$ cuts the circle $x^2+y^2+2x+2fy=0$ orthogonally, then $f=$

If the circles $x^2+y^2-16x-20y+164=r^2$ $(r>0)$ and $x^2+y^2-8x-14y+29=0$ intersect in two distinct points,then the maximum possible integral value of $r$ is

If the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p$,where $0 < p < a$,is $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$,then $\lambda=$

The point which has the same power with respect to each of the circles $x^2+y^2-8x+40=0$,$x^2+y^2-5x+16=0$,and $x^2+y^2-8x+16y+160=0$ is