Answer:
[tex]BG = 10cm[/tex]
Step-by-step explanation:
The intersection of all three perpendicular bisector is called the circumcenter, which is an equidistant point from each vertex of the triangle, that is
[tex]AG \cong CG \cong BG[/tex]
So, to find the answer, we just have to find the length of CG, and that would be also the length of BG.
Now, let's focus in the [tex]\triangle GFC[/tex], which is a right triangle and CG is the hypothenuse, applying pythagorean's theorem, we have
[tex]CG^{2}=CF^{2}+FG^{2}[/tex]
But, we know that [tex]CF=8;FG=6[/tex]
Replacing this values, we have
[tex]CG^{2}=8^{2}+6^{2}\\CG=\sqrt{64+36}=\sqrt{100}\\ CG=10[/tex]
Remember that [tex]CG = BG[/tex]
Therefore, [tex]BG = 10cm[/tex]
