In the given figure, AD is a median of ΔABC and E is the mid-point of AD. If BE is joined and produced to meet AC in F, then AF = ?

Question

Philoid · Accepted Answer

Let G be the mid-point of FC and join DG

In ∆BCF,

G is the mid-point of FC and D is the mid-point of BC

Thus, DG|| BF

DG || EF

Now, In ∆ ADG,

E is the mid-point of AD and EF is parallel to DG.

Thus, F is the mid-point of AG.

AF = FG = GC [G is the mid-point of FC]

Hence, AF = AC

∴ Option B is correct