Question

DG¯¯¯¯¯¯ , EG¯¯¯¯¯ , and FG¯¯¯¯¯ are perpendicular bisectors of the sides of △ABC . DG=5 cm and BD=12 cm.

Answer 1

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


`BG= √(DG^2+BD^2) \\ \\ = √(5^2+12^2) = √(25+144) \\ \\ = √(169) =13`

Since AG = BG = CG, therefore, CG = 13 cm.