Answer:
9
Step-by-step explanation:
A perpendicular bisector of a triangle is a line that is perpendicular to the side and passes through the midpoint of the triangle.
So when three perpendicular bisectors of the sides of a triangle meet at a point in a triangle, that point is called a circumcenter.
From the circumcenter theorem, we know that the circumcenter is equidistant from the vertices of a triangle, that is, the circumcenter is the same distance from each of the vertices of the triangle.
Looking at the given triangle, we can see that G is the circumcenter of the triangle because all the perpendicular bisectors DG, EG, and FG meet at this point.
We can see that AG is 9 which is the distance from vertex A to the circumcenter, G, since the circumcenter is equidistant from the vertices of a triangle according to the circumcenter theorem, therefore, BG will also be 9.