Final answer:
BD must be 8 centimeters because the circumcenter (point G) of triangle ABC is equidistant from all vertices, which makes GD equal to AD, the given length of which is 8 centimeters.
Step-by-step explanation:
The question asks about the properties of a circumcenter in a triangle, which is a Geometry concept relevant to high school mathematics. Given that point G is the circumcenter of triangle ABC, it implies that GD is equal to AD since the circumcenter is equidistant from all vertices of the triangle. Since AD is given as 8 centimeters, then BD must also be 8 centimeters because BD is the remainder of the diameter of the circumcircle when AD is subtracted from it (the diameter of the circumcircle being twice the radius, which is AD).