In ΔABC, median AD, BE, and CF intersect at G. If CF = 24, what is the value of FG?
- 8
- 10
- 12
- None of these
Explanation
Given CF = 24 and the centroid G divides CF in a 2:1 ratio, with the longer part toward the vertex C and the shorter part toward the midpoint F of side AB.
The total length CF is divided into 3 parts, where 2 parts are toward the vertex (CG) and 1 part is toward the midpoint (FG).
FG = (1/3) × CF = (1/3) × 24 = 8.
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