Return x; y; coordinates of vertex C of triangle
You can get the coordinates of C by using circle equations for one circle C_A with point A as center and AC as its radius and one circle C_B with point B as its center and BC as its radius.

Now you can calculate their intersection points, which leaves you with 2 points (iff C is not on a line between A and B).

I am not entirely sure how you want to determine which of the two candidates C_1 and C_2 is the correct one. If I understand correctly, you always label the triangle counterclockwise. There is a neat way to check this, so you should have everything to find your point.