The radical axis of two circles and the line joining their centres are

Let $C_1, C_2$ be two circles touching each other externally at the point $A$ and let $A B$ be the diameter of circle $C_1$. Draw a secant $B A_3$ to circle $C_2$, intersecting circle $C_1$ at a point $A_1(\neq A)$, and circle $C_2$ at points $A_2$ and $A_3$. If $B A_1=2, B A_2=3$ and $B A_3=4$, then the radii of circles $C_1$ and $C_2$ are respectively

The circles $x^2 + y^2 + 2x -2y + 1 = 0$ and $x^2 + y^2 -2x -2y + 1 = 0$ touch each  other :-

The gradient of the radical axis of the circles ${x^2} + {y^2} – 3x – 4y + 5 = 0$ and $3{x^2} + 3{y^2} – 7x + 8y + 11 = 0$ is

The condition that the circle ${(x – 3)^2} + {(y – 4)^2} = {r^2}$ lies entirely within the circle ${x^2} + {y^2} = {R^2},$ is