Figure 1 is a geometric query tool made of steel wire, in which △ABC is inscribed with ⊙G, AB is the diameter of ⊙G, AB=6, and AC = 3. Now the geometric query tool is placed in a plane rectangular coordinate system (as shown in Figure 2), and then point A slides to the right from point O on ray OX, and point B slides to point O on ray OY.

(1) try to explain that the original point o is always on ⊙G during the movement;

⑵ Let the coordinates of point C be (,), try to sum the functional relationship and write the range of independent variables;

(3) What is the movement distance of point C during the whole movement?