BG ≅ AG
BG is the perpendicular to the side of the triangle while AG is the angle bisector , So BG cannot equal AG , So BG cannot be congruent to AG. Hence first is false.
DG ≅ FG
DG And FG both are the perpendicular to the sides from the incentre of the circle , Hence DG and FG are congruent , So second statement is true.
DG ≅ BG
Again DG and BG both are the perpendicular to the sides from the incentre of the circle , Hence DG and BG are congruent , So third statement is true.
GE bisects ∠DEF
As said in the question GE is the angle bisector , So yes GE bisects ∠DEF.
This Statement is true.
GA bisects ∠BAF
Again As said in the question GA is the angle bisector , So yes GA bisects ∠BAF.
Hence 2nd, 3rd , 4th , and 5th options are correct.
