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In triangle ABC, D is the centroid and M is the midpoint of segment AC. If BD=x+9 and DM=6, find MB.

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the centroid divides any median in the ratio of 2:1, the shorter part towards the side.
so...
(x+0):6 = 2:1
.
.
x = 3
then BD = 3+9 = 12
so MB = BD + DM = 18

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