Because BF = df
So bo = do
It is easy to know that triangle DFO is similar to triangle ABD.
So DO/AD=DF/BD
That is, 7/ 10 = DF/ 14 and DF = 49/5.
Because he divided DBC equally.
So < CBE = < FBG = 1/2.
So BG split the FBD equally.
So DG/FG=BD/BF.
That is, DG/(49/5-DG) = 14/(49/5) and DG = 98/ 17.
Ask if you don't understand.