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In the given figure, AD is a median of ΔABC and E is the midpoint of side AD. If BE is joined and produced such that it meets AC in F, then find the relation between AF and AC.

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An Intiative by Sri Chaitanya

A F = 12 A C

A F =

13 A C

A F =

14 A C

A F =

23 A C

answer is B.

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Detailed Solution

Given that AD is a median of ΔABC and E is the midpoint of side AD. BE is joined and produced such that it meets AC in F.
Let G be the midpoint of CF and then join DG.
Question Image

Consider the

Δ B C F

, G is the mid-point of FC and we are given that D is the midpoint of BC.
Thus,

D G | | B F

.
In

Δ A D G,

E is the midpoint of AD.
Also, EF is parallel to DG.
Thus, F is the mid-point of AG.

A F = F G F G = G C

[As G is the mid-point of FC]
Thus, side AC is divided into three equal parts.
Hence,

A F = 13 A C

.
So, option 2 is the correct choice.

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