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Question

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?

This question was previously asked in
CDS I 2017 General Knowledge Previous Year Paper (05-Feb-2017)
The correct answer is

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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