The length of the common chord of the circles $x^2+y^2-6x-4y+9=0$ and $x^2+y^2-8x-6y+23=0$ is

Two circles which touch both the coordinate axes intersect at the points $A$ and $B$. If $A=(1,2)$,then $AB=$

If the chord of contact of tangents from a point on the circle $x^2+y^2=r_1^2$ to the circle $x^2+y^2=r_2^2$ touches the circle $x^2+y^2=r_3^2$,then $r_1, r_2, r_3$ are in:

Tangents are drawn from $(4, 4)$ to the circle $x^2 + y^2 - 2x - 2y - 7 = 0$ to meet the circle at $A$ and $B$. The length of the chord $AB$ is

Choose the correct option regarding the following statements :
Statement $I$: The length of the common chord of the circles $x^2+y^2+ax+by+c=0$ and $x^2+y^2+bx+ay+c=0$ is equal to $\frac{\sqrt{(a+b)^2-8c}}{2}$.
Statement $II$: If two circles intersect at two distinct points,then their radical axis is their common chord.

If $\frac{2}{\sqrt{5}}$ is the length of the common chord of the circles $x^2+y^2+2x+2y+1=0$ and $x^2+y^2+\alpha x+3y+2=0, \alpha \neq 0$,then $\alpha=$