Final answer:
The circumcenter of a triangle is found by constructing perpendicular bisectors of the sides and locating their point of intersection. The provided reference information is not related to the calculation of the circumcenter for this specific triangle.
Step-by-step explanation:
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter of the triangle with vertices A(2,5), B(6,6), and C(12,3), we must construct the perpendicular bisectors for at least two sides and find their intersection point. This can be achieved by using the midpoint formula to find the midpoint of two sides, and then deriving the slope of the perpendicular bisector since it is the negative reciprocal of the slope of the side segment. We then can write the equation of two perpendicular bisectors in the slope-intercept form (y = mx + b) and find their intersection by solving these two equations simultaneously.
However, the information provided in the question and reference information does not directly apply to this problem, so we will not use it in our computation of the circumcenter for the triangle defined by vertices A, B, and C.