Explanation:
I just answered this. how often did you post it ?
the "incenter" means that this is the center point of the inscribed circle that is completely inside the triangle and touches every side in exactly one point.
therefore, all right-angled connections from that point to a side are equally long (the radius is the inscribed circle).
therefore,
GB = GF = GD
we know GF = 22
so, GB = 22
and now we use Pythagoras to find AG in the right-angled triangle ABG :
AG² = AB² + GB² = 32² + 22² = 1024 + 484 = 1508
AG = sqrt(1508) = 38.83297568...
if you round to hundredths : 38.83