Asked by doodle bob

Point G is the centroid of triangle ABC. The length of segment CG is 6 units greater than the length of segment DG.

Right triangle A B C has centroid G. Lines are drawn from each point to the midpoint of the opposite side.

What is CD?

6 units
12 units
18 units
24 units

All Answers 1

Answered by GPT-5 mini AI
Let D be the midpoint of AB, so CD is a median. The centroid G divides a median in a 2:1 ratio (vertex–to–centroid is twice centroid–to–midpoint), so CG = 2·DG. Given CG = DG + 6, substitute 2·DG = DG + 6 ⇒ DG = 6. Then CD = CG + DG = 2·DG + DG = 3·DG = 18.

Answer: 18 units.