In triangle ABC, the medians AD and BE intersect at G. A line DF is drawn parallel to BE such that F is on AC. If AC = 9 cm, then what is CF equal to?
2.25 cm
Concept:
Median: A line segment that joins a vertex to the mid-point of the
the side that is opposite to that vertex
Basic proportionality theorem(BPT): If a line is drawn parallel to
one side of a triangle intersecting the other two sides in distinct
points, then the other two sides are divided in the same ratio.
Calculation:

Given that,
AD and BE are medians of BC and AC respectively.
⇒ BC = 2DC ------(1)
Also, we have AC = 9 cm
⇒ AE = EC = 9/2 = 4.5
In triangle CBE, DF ∥ BE
Using the Basic proportionality theorem
⇒ \(\frac{DC}{BC} = \frac{FC}{EC}\)
⇒ \(\frac{DC}{2DC} = \frac{FC}{4.5}\)
⇒ FC = 4.5/2 = 2.25 cm
∴ CF = 2.25 cm.
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