ABC is an isosceles triangle with angle A = 120 degrees. If G is the centroid of the triangle, and AD is the median, then find BG/DG.
See the following image :
Let B =(-sqrt (3) , 0) A = (0, 1) C = ( sqrt (3), 0 )
The centroid occurs at the intersection of the medians = G
Let BE be the median drawn to AC
cot (EBC) = (sqrt (3) + sqrt (3)/2 ) / (1/2) = [ 3sqrt (3) / 2] / (1/2) = 3sqrt(3) = BD/DG