Which of the following statements is/are correct?

If A,B,C are the centres of three circles touching mutually externally then the radical centre of the circles is incentre of triangle ABC

ABC is a triangle, the radical centre of the circles with AB,BC,CA as the diameters is orthocentre of triangle ABC

A,B,C are the centre of the three circles $C_1,C_2,C_3$ respectively such that $C_1,C_2$ touch other externally and they both touch $C_3$ from inside then radical centre of the circles is excentre opposite to vertex C

A,B,C are the centre of the three circles $C_1,C_2,C_3$  respectively such that $C_1,C_2$ touch other externally and they both touch $C_3$ from inside then radical centre of the circles is excentre opposite to vertex A