Let d be the distance from A to B. If you know A and B you can find its mid-point M. Lets say the vector AB is <s,t>. Then a vector perpendicular to it is <-t,s>. Divide that vector by its length and call the resulting vector V. If you know the radius r you can calculate the height h of your triangle with the Pythagorean theorem using hypotenuse r and leg d/2.
Then if O is the origin, the coordinates of the center are OA+ (1/2)ABą hV, with the sign chosen depending on which side of AB the center is on.