Answer:
[tex]AG=5\ cm[/tex]
Step-by-step explanation:
we know that
The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter (point G)
The circumcenter is equidistant from the vertices of the triangle
so
AG=CG=BG
Find the length side BG
In the right triangle BGE
Applying the Pythagorean Theorem
[tex]BG^2=GE^2+BE^2[/tex]
substitute the given values
[tex]BG^2=4^2+3^2[/tex]
[tex]BG^2=25[/tex]
[tex]BG=5\ cm[/tex]
therefore
[tex]AG=5\ cm[/tex]
