Q. 16 A4.0( 8 Votes )

# In the triangle ABC, AD and BE are two medians and DF parallel to BE, meets AC at the point F. If the length of the side AC is 8 cm., then let us write the length of the side CF.

Answer :

We extend the median AD till H such that GE||CH

In Δ BEC, BD = DC and BF||DG, therefore D is midpoint of BC,

By applying theorem:-

Through the mid-point of any side, if a line segment is drawn parallel to second side, then it will bisect the third side and the line segment intercepted by the two sides of the triangle is equal to half of the second side.

Also, as E is midpoint of AC,

From above two equations, we get

∴ length of FC is 2 cm

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