The centre of the smallest circle which cuts the circles $x^2+y^2-2 x-4 y-4=0$ and $x^2+y^2-10 x+12 y+52=0$ orthogonally is

If the poles of the line $x-y=0$ with respect to the circles $x^2+y^2-2 g_i x+c_i^2=0(i=1,2,3)$ are ( $\alpha_i, \beta_i$ ), then $\sum_{i=1}^3 \frac{\alpha_i+\beta_i}{g_i}=$

If a circle of radius $r$ touches the positive coordinate axes and also the circle $x^2+y^2-12 x-10 y+52=0$ externally, then the distance between the centres of the two circles is

If the circles $x^2+y^2-2 x-2 y+k=0$ and $x^2+y^2+4 x+6 y+4=0$ touch each other externally, then the point of contact of the two circles is