Given data:
The given triangle.
If G is the incentre of the given circle then,
GD=GE=GF
In triangle GDC.
It means GD=GE=GF=12.
In triangle BEG.
In triangle FGC.
Similarly BF=6, as triangle BEG is congruent ot the triangle BFG.
Thus, GD=12, BG=(180)^(1/2), FC=35, and BF=6.