Properties of Radical Axis

Q. Let $S_1$ and $S_2$ be two circles touching externally and having radius as $2$ and $3$ respectively. $S_1$ and $S_2$ touch a variable circle $S_3$ internally at $A$ and $B$ respectively. If the tangents to $S_3$ at $A$ and $B$ meet at $T$ and $TA=4\text{units}$, then which of the following is/are correct?
(Here, $C_i$ represents the centre of circle $S_i$)

1. The radius of circle $S_3$ is $8$ units.
2. The area of circle circumscribing $△TAB$ is $20\pi$ sq. units.
3. $C_3{C}_1+C_3{C}_2=5$
4. $C_3{C}_1–C_3{C}_2=1$

Q.

Which of the following statements is/are correct?

1. The radical axis of two circles is the locus of points whose power with respect to the two circles is equal.

2. The common point of intersection of the radical axes of three circles taken two at a time called the radical center of three circles.

1. Only 1

2. Only 2

3. Both 1 and 2

4. None of these