Question

In a triangle ABC, D is the mid-point
of BC and E is mid-point of AD,
BF passes through E. What is
the ratio of AF: FC ?
(a) 1:1
(b) 1:2
(C) 1:3
(d) 2:3 ​

Answer 1

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Answer 2

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CONSTRUCTION: DG ║ BF  (where 'G' is a point at AC )

In triangle ADG,

AE = ED ( given)

EF ║DG ( by construction)

So AF = FG……. ………(1) (a line passing through the mid point of any side of a triangle, parallel to the other side, bisects the third side)

Now in triangle CBF

BD = DC ( given)

DG ║ BF ( by construction)

So, FG = GC ( Same reason) ……..(2)

Now, by (1) & (2)

AF = FG = GC

=> AF : FC = 1:2

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