When is the angle of intersection of two circles $0^{\circ}$?

Three circles of radii $a, b, c$ $(a < b < c)$ touch each other externally. If they have the $x$-axis as a common tangent,then:

If the parametric values of two points $A$ and $B$ on the circle $x^2+y^2-6x+4y-12=0$ are $30^{\circ}$ and $90^{\circ}$ respectively,then the equation of chord $AB$ is

If one of the diameters of the circle given by the equation $x^{2}+y^{2}+4x+6y-12=0$ is a chord of a circle $S$ whose centre is $(2,-3)$, then the radius of $S$ is:

The maximum area of a rectangle inscribed in the circle $(x+1)^{2}+(y-3)^{2}=64$ is

Tangent $L_1 \equiv 3x - 4y - 8 = 0$ and the chord $L_2 \equiv x + y - 1 = 0$ are at a distance of $2$ and $\sqrt{2}$ units respectively from the centre of a circle $S$. $(h, k)$ is the centre of $S$ such that $h^2 + k^2 = 13$. If the midpoint of the chord $L_2 = 0$ is $(\alpha, \beta)$ and the radius of the circle is $r$,then $\alpha + \beta + r =$