Answer:
5 units
Step-by-step explanation:
If DG, EG and FG are perpendicular bisectors of the sides of triangle ABC, then point G is the circumcenter of the triangle ABC and
BG = AG = CG as radii of the circumcirle.
Consider right triangle BEG. By the Pythagorean theorem,
[tex]BG^2=EG^2+BE^2\\ \\BG^2=4^2+3^2\\ \\BG^2 =16+9\\ \\BG^2=25\\ \\BG=5\ units[/tex]
This gives us that
AG = BG = 5 units
