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.

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