Given that DG, EG, and FG are perpendicular bisectors of the sides of △ABC, this means that the point of intersection, G, is the circumcenter of the triangle and hence AG, BG, and CG are equal.
Given that DG = 5 cm and BD = 12 cm, then
[tex]BG= \sqrt{DG^2+BD^2} \\ \\ = \sqrt{5^2+12^2} = \sqrt{25+144} \\ \\ = \sqrt{169} =13[/tex]
Since AG = BG = CG, therefore, CG = 13 cm.
