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In △ABC, GE=27 in. What is the length of BE¯¯¯¯¯? Enter your answer in the box. 81 in. An acute triangle A B C is drawn. E is the midpoint of side A C. Segment A E and segment C E are labeled with double tick mark. F is the midpoint of side A B. Segment A F and segment F B are labeled with single tick mark. D is the midpoint of side B C. Segment B D and segment C D are labeled with triple tick mark. Line segment A D and C F and B F are medians of the triangle. Medians intersect with each other at an interior point labeled as G.

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nobillionaireNobley
Recall that the centroid of a triangle (the point where the three medians intersect) divides each median into parts in the ratio 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex.

Thus, the ratio of segment EG to segment BG is 1 : 2

Therefore, given that segment EG = 27 in, then segment BG = 2(27) = 54 in. and segment BE = 27 + 54 = 81 in.

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