Nickomalchite
Nickomalchite Nickomalchite
  • 13-11-2017
  • Mathematics
contestada

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

DG EG and FG are perpendicular bisectors of the sides of ABC DG5 cm and BD12 cm class=
DG EG and FG are perpendicular bisectors of the sides of ABC DG5 cm and BD12 cm class=

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nobillionaireNobley
nobillionaireNobley nobillionaireNobley
  • 24-11-2017
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.

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