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In triangle ABC, D is the centroid and M is the midpoint of segment AC. If BD=10 and DM=2x+1, find MB. Answer choices: 2 , 9.5, or 15.

the centroid cuts the median in the ratio of 2:1, the shorter part towards the midpoint of the side.

so 10/2 = (2x+1)/1

solve to get x=2
so DM = 5 and MB = 5+10 = 15

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