In ace g is the centroid and be=12 find bg and ge

For the answer to the question above, uUnder this assumption, BE is a median. Along with any median, the centroid of a triangle is always located 2/3 of the way from the vertex to the midpoint of the opposite side, so the centroid G is 2/3 of the way from E to B. 
So we have GE = (2/3)BE. 

Furthermore, by segment addition, BG + GE = BE. 

Since BE = 9, GE = (2/3)(9) = 6. 
Then BG + 6 = 9, which gives BG = 3